《船舶采购、销售和运营 Ship Purchase, Sales and Operations》课程教学资源：Identifying the dynamic relationship between tanker freight rates and oil prices：In the perspective of multiscale relevance

Economic Modelling 42(2014)287-295 Contents lists available at ScienceDirect Economic Modelling ELSEVIER journal homepage:www.elsevier.com/locate/ecmod Identifying the dynamic relationship between tanker freight rates and CrossMark oil prices:In the perspective of multiscale relevance Xiaolei Sun*,Ling Tangb,Yuying Yang Dengsheng Wu.Jianping Li Institute of Policy and Management,Chinese Academy of Sciences,Beijing 100190.China Beijing University of Chemical Technology,Beijing 100029.China University of Chinese Academy of Sciences,Beijing 100049.China ARTICLE INFO ABSTRACT Article history: The tanker shipping market has been treated as the key extension of the world oil market and inevitably,its Accepted 30 June 2014 uncertainty is correlated to volatility of the oil market,besides supply and demand factors.Therefore,for Available online 30 July 2014 improving operational management and budget planning decisions,it is essential to understand the inherent Keywords: relevance between freight rates and crude oil prices.Taking time-dependent features into account,this paper focuses on the multiscale correlation between freight rates and oil prices.Given the complexity and mutability Multiscales Ensemble EMD of tanker freight rate process,this paper first extracts the intrinsic mode functions from the original data using Relevance the Ensemble Empirical Mode Decomposition model and then reconstructs two separate composite functions: Freight rate high-frequency and low-frequency components,plus the residual as the long-term trend.Secondly.correlations Oil price of the multiscale components of freight rates and oil prices are examined based on relevance structure.Empirical results show that tanker freight rates and oil prices exhibit different multiscale properties with true economic meaning and are significantly correlated in the medium and the long term when taking the relevance structure into account.These findings offer some useful information to better understand the correlations between these two markets and more importantly.propose a novel perspective to investigate the dynamic relationship between two markets. 2014 Elsevier B.V.All rights reserved. 1.Introduction decision-making for shipping assets under uncertainty (Batchelor et al.,2007:Engelen et al.,2006:Glen,2006:Kavussanos and Crude oil,as a vital strategic commodity,is traded across the globe Alizadeh,2002:Tvedt,1997).Basically,shipping cycles inherent in the and this involves massive transportation infrastructures,including maritime industry propel freight rates to be mean-reverting in the pipelines,tankers and storage facilities (Rodrigue et al,2006).Interna- long run(Stopford,2008:Tvedt,2003).Moreover,the assumption of tionally,tanker shipping is necessary to address the imbalances inelastic demand and elastic supply can basically explain the phenome- between oil supply and demand in different regions.Moreover,tanker non of both small and large volatilities clustering together because of shipping,as the central logistics,plays a crucial role in the management small changes in the market balance (Strandenes and Adland,2007). of the global supply chain in the oil industry(Alizadeh and Nomikos, Besides,oil is not only the commodity being transported,but is also an 2004:Cheng and Duran,2004).More importantly,tanker shipping is a essential component of the transportation cost.While oil prices may service that provides "special"utility to the oil market and adds value explain some of the variation and dynamics in maritime transport to oil by moving it from surplus to deficit areas (Mayr and Tamvakis costs,other factors are also at play(UNCTAD,2010).Although the 1999).Naturally,tanker shipping market can be treated as the key methods used to model the dynamics of freight rate processes vary in extension of the international oil market and inevitably.its uncertainty extant literature,the consensus is that freight rates are time-varying. is closely correlated to volatility of the oil market,besides tanker supply non-linear and local non-stationary (Adland and Cullinane,2006; and demand.Spontaneously,for improving operational management and budget planning decisions,it is essential to investigate the inherent Summarized in UNCTAD(2010).These factors include.(a)demand for shipping services dynamic relationship between tanker freight rates and oil prices. (e.g.trade volumes):(b)port-level variables (e.g.the quality of port infrastructure): Much effort has gone into the study of modeling the dynamics of (c)product-level variables(e.g value/weight ratios and product prices):(d)industry-level tanker freight rates,in order to better support the operational variables(e.g.the extent of competition among shippers and carriers):(e)technological fac- tors(e.g the degree of containerization,size of ships and economies of scale):(f)institutional variables (e.g legislation and regulation):and (g)country-level variables (e.g attractiveness Corresponding author.TeL:+86 10 59358806 of export markets).This paper focuses on the relationship between oil price and freight rates, E-mail address:xlsun@casipm.accn (X.Sun). and specific analysis on these factors is beyond the scope of the present study. http://dx.doi.org/10.1016/j.econmod.201406.019 0264-99930 2014 Elsevier B.V.All rights reserved

Identifying the dynamic relationship between tanker freight rates and oil prices: In the perspective of multiscale relevance Xiaolei Sun a, ⁎, Ling Tang b , Yuying Yang a,c , Dengsheng Wu a , Jianping Li a a Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China b Beijing University of Chemical Technology, Beijing 100029, China c University of Chinese Academy of Sciences, Beijing 100049, China article info abstract Article history: Accepted 30 June 2014 Available online 30 July 2014 Keywords: Multiscales Ensemble EMD Relevance Freight rate Oil price The tanker shipping market has been treated as the key extension of the world oil market and inevitably, its uncertainty is correlated to volatility of the oil market, besides supply and demand factors. Therefore, for improving operational management and budget planning decisions, it is essential to understand the inherent relevance between freight rates and crude oil prices. Taking time-dependent features into account, this paper focuses on the multiscale correlation between freight rates and oil prices. Given the complexity and mutability of tanker freight rate process, this paper first extracts the intrinsic mode functions from the original data using the Ensemble Empirical Mode Decomposition model and then reconstructs two separate composite functions: high-frequency and low-frequency components, plus the residual as the long-term trend. Secondly, correlations of the multiscale components of freight rates and oil prices are examined based on relevance structure. Empirical results show that tanker freight rates and oil prices exhibit different multiscale properties with true economic meaning and are significantly correlated in the medium and the long term when taking the relevance structure into account. These findings offer some useful information to better understand the correlations between these two markets and more importantly, propose a novel perspective to investigate the dynamic relationship between two markets. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Crude oil, as a vital strategic commodity, is traded across the globe and this involves massive transportation infrastructures, including pipelines, tankers and storage facilities (Rodrigue et al., 2006). Interna￾tionally, tanker shipping is necessary to address the imbalances between oil supply and demand in different regions. Moreover, tanker shipping, as the central logistics, plays a crucial role in the management of the global supply chain in the oil industry (Alizadeh and Nomikos, 2004; Cheng and Duran, 2004). More importantly, tanker shipping is a service that provides “special” utility to the oil market and adds value to oil by moving it from surplus to deficit areas (Mayr and Tamvakis, 1999). Naturally, tanker shipping market can be treated as the key extension of the international oil market and inevitably, its uncertainty is closely correlated to volatility of the oil market, besides tanker supply and demand. Spontaneously, for improving operational management and budget planning decisions, it is essential to investigate the inherent dynamic relationship between tanker freight rates and oil prices. Much effort has gone into the study of modeling the dynamics of tanker freight rates, in order to better support the operational decision-making for shipping assets under uncertainty (Batchelor et al., 2007; Engelen et al., 2006; Glen, 2006; Kavussanos and Alizadeh, 2002; Tvedt, 1997). Basically, shipping cycles inherent in the maritime industry propel freight rates to be mean-reverting in the long run (Stopford, 2008; Tvedt, 2003). Moreover, the assumption of inelastic demand and elastic supply can basically explain the phenome￾non of both small and large volatilities clustering together because of small changes in the market balance (Strandenes and Adland, 2007). Besides, oil is not only the commodity being transported, but is also an essential component of the transportation cost. While oil prices may explain some of the variation and dynamics in maritime transport costs, other factors are also at play1 (UNCTAD, 2010). Although the methods used to model the dynamics of freight rate processes vary in extant literature, the consensus is that freight rates are time-varying, non-linear and local non-stationary (Adland and Cullinane, 2006; Economic Modelling 42 (2014) 287–295 ⁎ Corresponding author. Tel.: +86 10 59358806. E-mail address: xlsun@casipm.ac.cn (X. Sun). 1 Summarized in UNCTAD (2010). These factors include, (a) demand for shipping services (e.g. trade volumes); (b) port-level variables (e.g. the quality of port infrastructure); (c) product-level variables (e.g. value/weight ratios and product prices); (d) industry-level variables (e.g. the extent of competition among shippers and carriers); (e) technological fac￾tors (e.g. the degree of containerization, size of ships and economies of scale); (f) institutional variables (e.g. legislation and regulation); and (g) country-level variables (e.g. attractiveness of export markets). This paper focuses on the relationship between oil price and freight rates, and specific analysis on these factors is beyond the scope of the present study. http://dx.doi.org/10.1016/j.econmod.2014.06.019 0264-9993/© 2014 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

288 X.Sun et aL Economic Modelling 42 (2014)287-295 Adland et al.,2008:Goulielmos,2009;Kavussanos,1996;Kavussanos frequencies by using the decomposition algorithm,Ensemble Empirical and Alizadeh,2002:Tvedt,2003:Xu et al.,2011).In brief,high complex- Mode Decomposition(EMD).Secondly,multiscale components are con- ity and mutability of the freight rate process make modeling of the structed in terms of low frequency,high frequency and residual,and ac- inherent dynamics a challenging task. cordingly,the economic meanings can be explored in three scales: Although a substantial amount of information is available on the short-term fluctuation,medium-term pattern and long-term trend. dynamics of tanker freight rates,few studies have centered on the Then,correlations between the multiscale components of oil price and time-dependent properties of tanker freight rates as well as their tanker freight rates are investigated under the relevance structure, relevance for oil prices.In related studies,Alizadeh and Nomikos which is different from previous works in terms of the overall dynamics (2004)investigated the causal relationship between WTI futures and of freight rates. price of imported oil considering transportation costs and found To sum up,this paper attempts to propose a new framework of evidence of the existence of a long-run relationship between freight multiscale relevance to analyze the inherent relationship between rates and oil prices in the US.Moreover,Hummels (2007)showed tanker freight rates and oil prices.Insights gained from the perspective that maritime freight rates are highly sensitive to changes in oil prices. of multiscales will help further clarify the inherent dynamics of freight In a related study,Mirza and Zitouna(2009)examined whether effects rates and offer more information of the time-dependent relevance of oil prices on transportation costs vary across different suppliers and with oil prices.The rest of this paper is organized as follows.Section 2 buyers and the results showed a low elasticity of the correlation describes the research methodology.Section 3 describes the data and between freight rates and oil prices,ranging from 0.088 for countries empirical results are presented in Section 4.Finally,conclusions and close to the United States to 0.103 for faraway countries.With focus directions for further research are given in Section 5. on the West African and U.S.Gulf Coast tanker shipping market. Poulakidas and Joutz(2009)examined lead-lag relationship between 2.Estimation methodology oil prices and tanker freight rates using cointegration and Granger causality analysis.Additionally,forces of supply and demand can make This section describes a three-step analysis framework,which the relationship between crude oil prices and spot tanker rates ambigu- involves intrinsic mode function (IMF)extraction,multiscale compo- ous (Glen and Martin,2005).Here the results showed that the effect of nent construction and multiscale relevance examined.In the proposed rise in real oil price on spot rate is negative and positive for 250,000 dwt framework,the dynamic relationship can be divided into three separate and 130,000 dwt tanker vessels,respectively.The ambiguous relation- scales:the long-term trend,medium-term pattern in low frequency and ship can be explained with two possible factors addressed in Glen and short-term fluctuation in high frequency,which has not been found in Martin (2005).First,oil prices rise when oil demand rises and this extant literature.The following subsections then give the detailed increases the demand for oil transportation which then generates a description of the three main steps. positive association.Second,oil price rise might be caused by a reduc- tion in oil supply,which implies a fall in demand for oil transportation 2.1.Step 1:IMFs extracted services and an expected fall in spot rates.Hence,both a positive and a negative correlation can be justified.This makes the dynamic relation- In order to extract components at different scales which are in differ- ship between freight rates and oil prices complicated. ent time-frequencies from the original time series data,we adopt the Generally,both the long-term self-correcting mechanisms and Ensemble EMD method which is an empirical,intuitive,direct and short-term fluctuations of freight rates work in tandem.The interplay self-adaptive data processing method designed especially for nonlinear between short-term,long-term or seasonal forces leads to complicated and non-stationary data and are different from the simple parametric and time-varying freight rate processes.Thus,we agree with Engelen models.Ensemble EMD is a fully functional procedure based on diffu et al.(2011)in that it is necessary to take up the time-dependent sion models?that can be used to identify and estimate functions that features when modeling formulation of freight rates.When considering govern the dynamics,as stated in previous research.Ensemble EMD is the inherent complexity and mutability mix of original time series,Li a substantial improvement of EMD and can better separate the scales et al.(2012)proposed a decomposition hybrid approach to divide the naturally by adding white noise series to the original time series and original data into a series of relatively simple but meaningful compo- then treating the ensemble averages as the true intrinsic modes nents according to the "decomposition and ensemble"principle (Huang et al,1998:Wu and Huang,2004). (Wang et al,2005;Yu et al.2008).These works inspire us to As an efficient tool for identifying multiscale properties,EMD and decompose the tanker freight rates into different scales in terms of Ensemble EMD have been widely used to extract true intrinsic modes time-frequency,which can offer more information of the inherent from complex objects in the reality (Cummings et al.,2004:Huang dynamic properties of freight rates.Moreover,it provides a novel et al,2003;Xie et al.,2008:Zhang et al,2008).In this paper,the decom- perspective to investigate the relationship between tanker freight position algorithm,Ensemble EMD model,is adopted to decompose the rates and oil prices. original data,x(t=1.2.....T).into n components ct(j=1.2....n).The According to the "decomposition and ensemble"principle,a process xt and cir satisfy Eq.(1). of decomposition can be performed to divide the original data of tanker freight rates into a series of relatively simple but meaningful compo- nents.Considering the dilemma between difficulties in modeling and (1) lack of economic meaning can be solved by some decomposition methods,Zhang et al.(2008)identified the economic meanings of the three components of oil prices.Similarly,we identify and define the where n-1 is the number of IMFs and cir(j=1,2....,n-1)denote the jth intrinsic mode function,which must satisfy the following two condi- economic meanings of the three components as long-term trend, tions:(1)in each whole function,the number of extrema (both maxima medium-term pattern in low frequency and short-term fluctuation in high frequency,which helps to understand the underlying rules of and minima)and the number of zero crossings must be equal or differ at the most by one;and (2)the intrinsic mode functions must be symmet- reality by exploring data's intrinsic modes. Of particular interest and novelty is to examine the inherent ric with respect to local zero mean.Besides,the nth component r is the relationship between oil prices and tanker freight rates by introducing final residual,which represents the central tendency of data series x. the concept and process of multiscale relevance.In the process of multiscale relevance,freight rates and oil prices can first be decomposed into intrinsic mode functions in the different and simple time Summarized in Adland and Cullinane (2006)and Adland et al (2008)

Adland et al., 2008; Goulielmos, 2009; Kavussanos, 1996; Kavussanos and Alizadeh, 2002; Tvedt, 2003; Xu et al., 2011). In brief, high complex￾ity and mutability of the freight rate process make modeling of the inherent dynamics a challenging task. Although a substantial amount of information is available on the dynamics of tanker freight rates, few studies have centered on the time-dependent properties of tanker freight rates as well as their relevance for oil prices. In related studies, Alizadeh and Nomikos (2004) investigated the causal relationship between WTI futures and price of imported oil considering transportation costs and found evidence of the existence of a long-run relationship between freight rates and oil prices in the US. Moreover, Hummels (2007) showed that maritime freight rates are highly sensitive to changes in oil prices. In a related study, Mirza and Zitouna (2009) examined whether effects of oil prices on transportation costs vary across different suppliers and buyers and the results showed a low elasticity of the correlation between freight rates and oil prices, ranging from 0.088 for countries close to the United States to 0.103 for faraway countries. With focus on the West African and U.S. Gulf Coast tanker shipping market, Poulakidas and Joutz (2009) examined lead–lag relationship between oil prices and tanker freight rates using cointegration and Granger causality analysis. Additionally, forces of supply and demand can make the relationship between crude oil prices and spot tanker rates ambigu￾ous (Glen and Martin, 2005). Here the results showed that the effect of rise in real oil price on spot rate is negative and positive for 250,000 dwt and 130,000 dwt tanker vessels, respectively. The ambiguous relation￾ship can be explained with two possible factors addressed in Glen and Martin (2005). First, oil prices rise when oil demand rises and this increases the demand for oil transportation which then generates a positive association. Second, oil price rise might be caused by a reduc￾tion in oil supply, which implies a fall in demand for oil transportation services and an expected fall in spot rates. Hence, both a positive and a negative correlation can be justified. This makes the dynamic relation￾ship between freight rates and oil prices complicated. Generally, both the long-term self-correcting mechanisms and short-term fluctuations of freight rates work in tandem. The interplay between short-term, long-term or seasonal forces leads to complicated and time-varying freight rate processes. Thus, we agree with Engelen et al. (2011) in that it is necessary to take up the time-dependent features when modeling formulation of freight rates. When considering the inherent complexity and mutability mix of original time series, Li et al. (2012) proposed a decomposition hybrid approach to divide the original data into a series of relatively simple but meaningful compo￾nents according to the “decomposition and ensemble” principle (Wang et al., 2005; Yu et al., 2008). These works inspire us to decompose the tanker freight rates into different scales in terms of time–frequency, which can offer more information of the inherent dynamic properties of freight rates. Moreover, it provides a novel perspective to investigate the relationship between tanker freight rates and oil prices. According to the “decomposition and ensemble” principle, a process of decomposition can be performed to divide the original data of tanker freight rates into a series of relatively simple but meaningful compo￾nents. Considering the dilemma between difficulties in modeling and lack of economic meaning can be solved by some decomposition methods, Zhang et al. (2008) identified the economic meanings of the three components of oil prices. Similarly, we identify and define the economic meanings of the three components as long-term trend, medium-term pattern in low frequency and short-term fluctuation in high frequency, which helps to understand the underlying rules of reality by exploring data's intrinsic modes. Of particular interest and novelty is to examine the inherent relationship between oil prices and tanker freight rates by introducing the concept and process of multiscale relevance. In the process of multiscale relevance, freight rates and oil prices can first be decomposed into intrinsic mode functions in the different and simple time frequencies by using the decomposition algorithm, Ensemble Empirical Mode Decomposition (EMD). Secondly, multiscale components are con￾structed in terms of low frequency, high frequency and residual, and ac￾cordingly, the economic meanings can be explored in three scales: short-term fluctuation, medium-term pattern and long-term trend. Then, correlations between the multiscale components of oil price and tanker freight rates are investigated under the relevance structure, which is different from previous works in terms of the overall dynamics of freight rates. To sum up, this paper attempts to propose a new framework of multiscale relevance to analyze the inherent relationship between tanker freight rates and oil prices. Insights gained from the perspective of multiscales will help further clarify the inherent dynamics of freight rates and offer more information of the time-dependent relevance with oil prices. The rest of this paper is organized as follows. Section 2 describes the research methodology. Section 3 describes the data and empirical results are presented in Section 4. Finally, conclusions and directions for further research are given in Section 5. 2. Estimation methodology This section describes a three-step analysis framework, which involves intrinsic mode function (IMF) extraction, multiscale compo￾nent construction and multiscale relevance examined. In the proposed framework, the dynamic relationship can be divided into three separate scales: the long-term trend, medium-term pattern in low frequency and short-term fluctuation in high frequency, which has not been found in extant literature. The following subsections then give the detailed description of the three main steps. 2.1. Step 1: IMFs extracted In order to extract components at different scales which are in differ￾ent time-frequencies from the original time series data, we adopt the Ensemble EMD method which is an empirical, intuitive, direct and self-adaptive data processing method designed especially for nonlinear and non-stationary data and are different from the simple parametric models. Ensemble EMD is a fully functional procedure based on diffu￾sion models2 that can be used to identify and estimate functions that govern the dynamics, as stated in previous research. Ensemble EMD is a substantial improvement of EMD and can better separate the scales naturally by adding white noise series to the original time series and then treating the ensemble averages as the true intrinsic modes (Huang et al., 1998; Wu and Huang, 2004). As an efficient tool for identifying multiscale properties, EMD and Ensemble EMD have been widely used to extract true intrinsic modes from complex objects in the reality (Cummings et al., 2004; Huang et al., 2003; Xie et al., 2008; Zhang et al., 2008). In this paper, the decom￾position algorithm, Ensemble EMD model, is adopted to decompose the original data, xt (t = 1, 2,…, T), into n components cj,t (j = 1, 2,…, n). The xt and cj,t satisfy Eq. (1). xt ¼ Xn−1 j¼1 cj;t þ rt ð1Þ where n-1 is the number of IMFs and cj,t (j = 1, 2,…, n-1) denote the jth intrinsic mode function, which must satisfy the following two condi￾tions: (1) in each whole function, the number of extrema (both maxima and minima) and the number of zero crossings must be equal or differ at the most by one; and (2) the intrinsic mode functions must be symmet￾ric with respect to local zero mean. Besides, the nth component rt is the final residual, which represents the central tendency of data series xt. 2 Summarized in Adland and Cullinane (2006) and Adland et al. (2008). 288 X. Sun et al. / Economic Modelling 42 (2014) 287–295

X.Sun et al Economic Modelling 42 (2014)287-295 289 189 3500.00 BDTI 140.00 3000.00 120.00 2500.00 100.00 2000.00 80.00 1500.00 60.00 000.00 40.00 20.00 s00.00 03.1w五 Fig.1.Time series of the original BDTI and WTI. 2.2.Step 2:Multiscale component constructed speaking,the high-frequency component refers to a fluctuating process in the short run and the low-frequency component implies a slowly vary- Although IMFs contained in each frequency band are different and ing trend.Additionally,the residual is treated separately as it reflects the they change with variation of time series x.what we focus on actually long-term trend.These three components corresponding to different is to explore IMFs of similar characteristics.Thus,the fine-to-coarse time-frequency trends reveal some underlying features of the original reconstruction algorithm is used to construct two separate composite data.Spontaneously,a question arises:which component is the most functions:high-frequency and low-frequency components. important scale,e.g.major scale? Firstly,superposition sum for the ith IMF is calculated using the func- In order to answer this question,variances of IMFs,residual and tion sit=>=Ckr Secondly,the structural change point P is tested by T original data are calculated and denoted as Vc.Vr and Vob.Then. statistics where the mean of st is farthest from zero and then let P=i. variance percentage and variability percentage of each component can Finally,the high-frequency component involving from cir to cp-1t is be measured by: reconstructed by Highf=>ck while the low-frequency component involving other IMFs is reconstructed by Lowf=>ck.The residual Vci Variability percentage vpCi= ∑G+M,pr= >VG+Vr (2) is denoted as Res.and the three components are obtained.Generally 200 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 200 -200 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 500 ww-ww wohwyio -500 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 500 -98080 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 兰 500 T -500 198.08.03 2000.08.16 2002.09.01 2004.0922 2007.04.12 2009.06.16 201L.x.08 1000 0 T T T 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 201.0808 500 入 T 9080 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 入 0 -500 1998.08.03 2000.08.16 2002.09.01 2004.09,22 2007.04.12 200906.16 2011.08.08 20 f 7 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 0 1 -50 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 1500 1000 500 1998.08.03 2000.08.16 20W02.09.01 2004.09.22 2007.04.12 2009.06.16 2011.8.D8 Fig.2.The IMFs and residual of original BDTL

2.2. Step 2: Multiscale component constructed Although IMFs contained in each frequency band are different and they change with variation of time series xt, what we focus on actually is to explore IMFs of similar characteristics. Thus, the fine-to-coarse reconstruction algorithm is used to construct two separate composite functions: high-frequency and low-frequency components. Firstly, superposition sum for the ith IMF is calculated using the func￾tion si,t =∑k=1 i ck,t. Secondly, the structural change point P is tested by T statistics where the mean of si,t is farthest from zero and then let P=i. Finally, the high-frequency component involving from c1,t to cP−1,t is reconstructed by Highf =∑k=1 P−1 ck,t while the low-frequency component involving other IMFs is reconstructed by Lowf = ∑k=P n−1 ck,t. The residual is denoted as Res. and the three components are obtained. Generally speaking, the high-frequency component refers to a fluctuating process in the short run and the low-frequency component implies a slowly vary￾ing trend. Additionally, the residual is treated separately as it reflects the long-term trend. These three components corresponding to different time–frequency trends reveal some underlying features of the original data. Spontaneously, a question arises: which component is the most important scale, e.g., major scale? In order to answer this question, variances of IMFs, residual and original data are calculated and denoted as Vci, Vr and Vob. Then, variance percentage and variability percentage of each component can be measured by: Variability percentage : vpci ¼ Vc X i Vci þ Vr ; vpr ¼ X Vr Vci þ Vr : ð2Þ 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 1998-8-3 1999-8-3 2000-8-3 2001-8-3 2002-8-3 2003-8-3 2004-8-3 2005-8-3 2006-8-3 2007-8-3 2008-8-3 2009-8-3 2010-8-3 2011-8-3 WTI Original WTI BDTI Original BDTI Fig. 1. Time series of the original BDTI and WTI. Fig. 2. The IMFs and residual of original BDTI. X. Sun et al. / Economic Modelling 42 (2014) 287–295 289

290 X.Sun et aL Economic Modelling 42 (2014)287-295 4000 Highf Lowf 3000 --Res. --Original BDTI 2000 1000 人M心 -1000 1998.08D3 2000.08.16 202.090T 2004.09.22 2007.04.12 2009.06.16 2011.08.08 2000 wn人fbohfno 9908.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 Fig.3.Multiscale components of original BDTI. It is to be noted that equation Vc +Vr Vob does not always components of tanker freight rates (TFR)and oil prices (OP)can be hold because of a combination of rounding errors,nonlinearity of generalized by the simplification: original time series and introduction of variance by the treatment of the cubic spline end conditions(Peel et al.,2005).With the correlations relevance=F(CTFR Cop.RcRs) (4) between each component and original data,the component with the highest correlation coefficients and variance and variability percentage where Cr denotes the multiscale components of tanker freight rates can be identified as the major scale,which determines the major and CTER =(HighfTER.LowfTER,Res.TER):Cop is the multiscale components trend of the dynamics of the original data. ofoil price and Cop=(Highfor Lowfop Res.op):Rc describes the relevance as measured by correlation coefficients under a certain relevance structure Rs. 2.3.Step 3:Multiscale relevance examined Relevance level between multiscale components of tanker freight rates and oil prices is examined by using two correlation coefficients. Time series of tanker freight rates and oil prices exhibit changes over Pearson's y linear coefficient and Kendall's T rank coefficient,which time.This not only leads to the relevance level changing.but also results measure the correlations from different points of view.Nevertheless, in the structural changes.such as the relevance from positive to it is worth noting that the relevance level or structure may change in negative structure.To gain a better understanding of the inherent the sample period.In this paper,we try to identify which component's relevance of components at different scales,the relevance structure is relevance is of the highest correlations,and then analyze the relevance introduced,besides the relevance level.Given that relevance is a structure between the corresponding components.If the relevance relationship between two entities of two groups,the relevance between structure is changed,the whole sample can be divided into different High --Res. .-·0 riginal W1 9808.01 200008.16 202.09.01 2004.0922 200m.M.12 2009.06.16 20110s08 Highf -10 2002.09.01 2004.22 207.D4.12 2009,6.16 2011040% Fig.4.Multiscale components of original WTI

It is to be noted that equation ∑ Vci + Vr = Vob does not always hold because of a combination of rounding errors, nonlinearity of original time series and introduction of variance by the treatment of the cubic spline end conditions (Peel et al., 2005). With the correlations between each component and original data, the component with the highest correlation coefficients and variance and variability percentage can be identified as the major scale, which determines the major trend of the dynamics of the original data. 2.3. Step 3: Multiscale relevance examined Time series of tanker freight rates and oil prices exhibit changes over time. This not only leads to the relevance level changing, but also results in the structural changes, such as the relevance from positive to negative structure. To gain a better understanding of the inherent relevance of components at different scales, the relevance structure is introduced, besides the relevance level. Given that relevance is a relationship between two entities of two groups, the relevance between components of tanker freight rates (TFR) and oil prices (OP) can be generalized by the simplification: relevance ¼ F CTFR; COP ðÞ ð ; RcjRs 4Þ where CTFR denotes the multiscale components of tanker freight rates and CTFR = (HighfTFR, LowfTFR, Res.TFR); COP is the multiscale components of oil price and COP = (HighfOP, LowfOP, Res.OP); Rc describes the relevance as measured by correlation coefficients under a certain relevance structure Rs. Relevance level between multiscale components of tanker freight rates and oil prices is examined by using two correlation coefficients, Pearson's γ linear coefficient and Kendall's τ rank coefficient, which measure the correlations from different points of view. Nevertheless, it is worth noting that the relevance level or structure may change in the sample period. In this paper, we try to identify which component's relevance is of the highest correlations, and then analyze the relevance structure between the corresponding components. If the relevance structure is changed, the whole sample can be divided into different Fig. 3. Multiscale components of original BDTI. Fig. 4. Multiscale components of original WTI. 290 X. Sun et al. / Economic Modelling 42 (2014) 287–295

X.Sun et al Economic Modelling 42 (2014)287-295 291 Original BDTI Res.of BDTI 3500 3500 000 3000 2500 2000 1500 1000 500. 1998.08.03 2011.08.08 1998.08.03 2011.08.08 Highf of BDTI Lowf.of BDTI 1600 1600 1998.08.03 1998.08.03 2011.08.08 Fig.5.The original BDTI.its omponents. and the average. periods,and then relevance changes in different sub-samples can be Index),published by the Baltic Exchange.The BDTI represents tanker analyzed since the structure evolves in time. routes of crude oil while the BCTI covers tanker routes of oil derivatives (gasoline,benzene,etc.).The indices are defined as the sum of multipli- cations of the average rate for each route with the weighted factor of 3.Data description that particular route.The dynamics of the two indices are affected by In the present study,available data cover the period from August 3. some common cost determinants and are highly correlated.Considering 1998 to September 29,2011 and consist of daily observations on the the focus on crude oil transportation,we select the BDTI as the bench- following variables:price of West Texas Intermediate crude oil(WTI) mark of crude oil tanker freight rates. and Baltic Dirty Tanker Index(BDTI),as shown beneath in Fig.1,with- As shown in Fig.1,time series of the original BDTI and WTI exhibit a out the missing data.The former are obtained from the website of U.S. similar trend in some long periods,while short-term volatilities are Energy Information Administration,and the latter are obtained from irregular and different.This similarity allows us to explore the dynamic the Baltic Exchange. relationship between these two markets from the perspective of multiscales. Nowadays,in the international oil market,West Texas Intermediate (WTI)is a type of crude oil used as a benchmark in oil pricing.as the un- derlying product of New York Mercantile Exchange's oil futures con- 4.Empirical results tracts.Actually,WTI oil price has high correlation with Brent oil price and OPEC Basket oil prices,which are also important benchmarks in In this section,firstly,multiscale components of the BDTI and WTI oil pricing.Hence,we take WTl oil price as a proxy of international are extracted and analyzed;then relevance of the different scales is crude oil price.The tanker shipping market is described by two indices: modeled and the results are further discussed. the BDTI(Baltic Dirty Tanker Index)and the BCTI(Baltic Clean Tanker 4.1.Extracting the multiscale components Firstly,the original BDTI series can be decomposed into a set of inde- Table 1 pendent IMFs by performing the Ensemble EMD algorithm3.Ten IMFs Statistical measures of the components for the original BDTI and WTI series. are listed in the order in which they are extracted,that is,from the Components BDTI wn highest frequency to the lowest frequency,and the last is the residual Highf Lowf Res. Highf Lowf Res. (shown in Fig.2). Then,the IMFs are separated into two parts through the fine-to-coarse Mean period 5.73 506.17 3.65 79.92 Pearson'sy 0.58 0.70* 0.42* 008 0.71* 0.85* reconstruction algorithm.The partial reconstruction with IMF1 to IMF5 Kendall's T 0.21* 0.52* 0.30* 0.06 039* 0.75* Variance percentage 24.96% 45.63% 20.05%0.43% 1881% 54.53% Variability percentage 27.54% 50.34%22.12%0.58%25.50% 73.92% In the Ensemble EMD.anensemble member of 100isused,and the added white noise Correlation is significant at the 0.05 level (2-tailed). in each ensemble member has a standard deviation of 0.2

periods, and then relevance changes in different sub-samples can be analyzed since the structure evolves in time. 3. Data description In the present study, available data cover the period from August 3, 1998 to September 29, 2011 and consist of daily observations on the following variables: price of West Texas Intermediate crude oil (WTI) and Baltic Dirty Tanker Index (BDTI), as shown beneath in Fig. 1, with￾out the missing data. The former are obtained from the website of U.S. Energy Information Administration, and the latter are obtained from the Baltic Exchange. Nowadays, in the international oil market, West Texas Intermediate (WTI) is a type of crude oil used as a benchmark in oil pricing, as the un￾derlying product of New York Mercantile Exchange's oil futures con￾tracts. Actually, WTI oil price has high correlation with Brent oil price and OPEC Basket oil prices, which are also important benchmarks in oil pricing. Hence, we take WTI oil price as a proxy of international crude oil price. The tanker shipping market is described by two indices: the BDTI (Baltic Dirty Tanker Index) and the BCTI (Baltic Clean Tanker Index), published by the Baltic Exchange. The BDTI represents tanker routes of crude oil while the BCTI covers tanker routes of oil derivatives (gasoline, benzene, etc.). The indices are defined as the sum of multipli￾cations of the average rate for each route with the weighted factor of that particular route. The dynamics of the two indices are affected by some common cost determinants and are highly correlated. Considering the focus on crude oil transportation, we select the BDTI as the bench￾mark of crude oil tanker freight rates. As shown in Fig. 1, time series of the original BDTI and WTI exhibit a similar trend in some long periods, while short-term volatilities are irregular and different. This similarity allows us to explore the dynamic relationship between these two markets from the perspective of multiscales. 4. Empirical results In this section, firstly, multiscale components of the BDTI and WTI are extracted and analyzed; then relevance of the different scales is modeled and the results are further discussed. 4.1. Extracting the multiscale components Firstly, the original BDTI series can be decomposed into a set of inde￾pendent IMFs by performing the Ensemble EMD algorithm3 . Ten IMFs are listed in the order in which they are extracted, that is, from the highest frequency to the lowest frequency, and the last is the residual (shown in Fig. 2). Then, the IMFs are separated into two parts through the fine-to-coarse reconstruction algorithm. The partial reconstruction with IMF1 to IMF5 0 500 1000 1500 2000 2500 3000 3500 Original BDTI 0 500 1000 1500 2000 2500 3000 3500 Res.of BDTI -800 -400 0 400 800 1200 1600 Highf of BDTI -800 -400 0 400 800 1200 1600 Lowf. of BDTI 1998.08.03 1998.08.03 1998.08.03 1998.08.03 2011.08.08 2011.08.08 2011.08.08 2011.08.08 Fig. 5. The original BDTI, its multiscale components, and the average. Table 1 Statistical measures of the components for the original BDTI and WTI series. Components BDTI WTI Highf Lowf Res. Highf Lowf Res. Mean period 5.73 506.17 – 3.65 79.92 – Pearson's γ 0.58⁎ 0.70⁎ 0.42⁎ 0.08⁎ 0.71⁎ 0.85⁎ Kendall's τ 0.21⁎ 0.52⁎ 0.30⁎ 0.06⁎ 0.39⁎ 0.75⁎ Variance percentage 24.96% 45.63% 20.05% 0.43% 18.81% 54.53% Variability percentage 27.54% 50.34% 22.12% 0.58% 25.50% 73.92% ⁎ Correlation is significant at the 0.05 level (2-tailed). 3 In the Ensemble EMD, an ensemble member of 100 is used, and the added white noise in each ensemble member has a standard deviation of 0.2. X. Sun et al. / Economic Modelling 42 (2014) 287–295 291

292 X.Sun et aL Economic Modelling 42 (2014)287-295 Table 2 4.2.Identifying the major scale Correlations between original WTI and multiscale components of the BDTI. Original BDTI Highf of BDTI Lowf of BDTI Res.of BDTI To answer which component is of the major scale,Table 1 gives Pearson's v 0.0655* 0.0987* 0.4170 -0.5753* statistical measures in which the mean period is the value derived by Kendall'sT 0.0695* 0.0504 0.3037* -0.3311* dividing the total number of points by the number of peaks.The periods Correlation is significant at the 0.05 level (2-tailed). of high-frequency components of the BDTI and WTI are close to each other,5.73 and 3.65 days,respectively,while periods of low-frequency components vary widely,506.17 and 79.92 days,respectively. For the BDTI,the low-frequency component has a high correlation represents the high-frequency component,the other IMFs are recon- with the original time series and accounts for more than 50%of total structed to represent the low-frequency component and the residual re- variability.The high-frequency component and the residual impact flects the long-term trend.Fig.3 shows the three components. the original tanker freight rates almost of the same extent but with dif- Similarly,ten IMFs of the WTI can be obtained;the partial recon- ferent performances.The proportion of variability of high-frequency struction with IMF1 to IMF4 represents the high-frequency component, component is a little higher than that of the residual,still accounting and IMF5 to IMF10 are reconstructed to represent the low-frequency for about 25%of total variability.All the three components show obvi- component and the residual.The three reconstructed components are ous correlations with the original BDTI,and taking correlation coeffi- shown below in Fig.4. cients into account,we can come to the conclusion that the low- Each component has some distinct characteristics.Among the differ- frequency component explains the highest proportion of the original ent time-frequency components of BDTI and WTI in Figs.3 and 4,one BDTI.In other words,the low-frequency component determines the common feature is that the residual basically reflects the trend level major scale of tanker freight rates.Meanwhile,high-frequency compo- and the low-frequency component more exactly describes the structur- nent and residual also provide explanation of a large proportion. al pattern of the original data.Specifically,the low frequency compo- Differently,crude oil price is practically determined by the long- nent of the BDTI varies slowly and smoothly,but corresponds to the term trend (that is,the residual).which accounts for more than 73%of cyclicality or seasonality patterns of the shipping market fluctuations. observed price variability.Next,the low-frequency component has a The high-frequency component of the BDTI,as mentioned before,is mean period of about 80 days and accounts for about 25%of total de-trended signals with drastic fluctuations and determines the short- variability,while its Pearson's y reaches a high level of 0.71,meaning term changes with large amplitudes.This feature of short-term volatili- that a linear correlation exists.However,the high-frequency component ty is different from oil price,which has a high-frequency component of just accounts for about 0.58%of total variability with a very low Pearson's very small amplitudes.One reason can be that the tanker shipping mar- coefficient.Thus,it is concluded that the long-term trend is the major ket is influenced by uncertainties of tanker capacity,shipbuilding and scale for oil price compared with the second important scale,e.g.,low- demolition market also,besides oil supply and demand frequency component.This feature has also been examined in Huang As shown in Fig.5,the dashed lines describe the average of original et al.(1998)and Zhang et al.(2008),and the residual is treated as the de- BDTI and its three components.The average of the original BDTI is about terministic long-term behavior. 1164,while that of BDTI residual is about 1155.There is little difference To sum up,the low-frequency component is the major scale of the between the two,so we take the residual as the average trend of the BDTI and the high-frequency and residual components are almost of BDTI.For high-frequency and low-frequency components,the average equal significance.For the time series of the WTL,the residual is the of both is close to zero,and this is rational for short-term fluctuation major scale and low-frequency component is the second important and medium-term cyclicality.These two components fluctuate due to scale,while the high-frequency component has hardly any role in the external shocks or supply-demand self-adjustment,and tend to determining the original WTI.More importantly,the residual of the move towards the average level.In other works,high-frequency and BDTI first increases and then decreases after the turning point,while low-frequency components fluctuate around dashed lines near zero. the residual of the WTI exhibits a trend of continued growth without since the average of BDTI has to be separated as the residual.In brief, any change in direction. this implies that in the tanker shipping market there is the obvious mean reversion in the long run which is a common feature of time 4.3.Analyzing the multiscale relevance between BDTI and WTI series. The consensus,therefore,is that freight rates are mean-reverting in In this subsection,the relevance between the BDTI and the WTl is the longer run as implied by the maritime economic theory (Adland our focus.At first,the correlation coefficients between original WTI oil and Cullinane,2006:Tvedt,2003).The potential for supply adjustment price and multiscale components of tanker freight rates are measured, (new building and demolition)in a competitive market guarantees that as shown in Table 2. extremely high or extremely low freight rates are not sustainable in the long run.Adland et al.(2008)concurred with Dixit and Pindyck(1994) 4.3.1.Relevance between multiscale components in that it is difficult to detect long-run mean reversion particularly when Intuitively,the correlation between WTI and BDTI over a long time using high-frequency data.However,it is convenient to examine the span is very low,with Pearson's coefficient of 0.065 and Kendall's long-run mean reversion even if the daily data is used in our study. coefficient of 0.0695.However,by dividing the original BDTI into three components,the behavior of correlation changes.Although the correla- tion between the original WTI and high-frequency component of the BDTI is also very low,the low-frequency component and the residual Correlations of multiscale components between the BDTI and WTl. are significantly correlated with the original WTI,in the opposite direction.The former is positive and the latter is negative.This suggests Correlations Pearson's y Kendall's T that it is necessary to decompose the original BDTI into different time- Components Highf of Res.of Highf of Res.of frequency components when exploring the relevance between the BDTl WTI WTI wIl WTI wn WTI and WTI,because it can offer more correlation information. Highf of BDTI 0.00 0.10* 0.07* 0.00 0.03* 0.06* For a detailed analysis of the relevance,we further calculate the co- Lowf of BDTI -0.01* 051* 0.21* -0.01* 035 0.14 efficients of correlation between multiscale components of BDTI and Res.of BDTI -0.02 -026 -0.60 -0.01 -037 -0.37 WTI(Table 3).The coefficients have characteristics similar to Table 1. Correlation is significant at the 0.05 level (2-tailed). For the BDTI,its high-frequency components show very low

represents the high-frequency component, the other IMFs are recon￾structed to represent the low-frequency component and the residual re- flects the long-term trend. Fig. 3 shows the three components. Similarly, ten IMFs of the WTI can be obtained; the partial recon￾struction with IMF1 to IMF4 represents the high-frequency component, and IMF5 to IMF10 are reconstructed to represent the low-frequency component and the residual. The three reconstructed components are shown below in Fig. 4. Each component has some distinct characteristics. Among the differ￾ent time–frequency components of BDTI and WTI in Figs. 3 and 4, one common feature is that the residual basically reflects the trend level and the low-frequency component more exactly describes the structur￾al pattern of the original data. Specifically, the low frequency compo￾nent of the BDTI varies slowly and smoothly, but corresponds to the cyclicality or seasonality patterns of the shipping market fluctuations. The high-frequency component of the BDTI, as mentioned before, is de-trended signals with drastic fluctuations and determines the short￾term changes with large amplitudes. This feature of short-term volatili￾ty is different from oil price, which has a high-frequency component of very small amplitudes. One reason can be that the tanker shipping mar￾ket is influenced by uncertainties of tanker capacity, shipbuilding and demolition market also, besides oil supply and demand. As shown in Fig. 5, the dashed lines describe the average of original BDTI and its three components. The average of the original BDTI is about 1164, while that of BDTI residual is about 1155. There is little difference between the two, so we take the residual as the average trend of the BDTI. For high-frequency and low-frequency components, the average of both is close to zero, and this is rational for short-term fluctuation and medium-term cyclicality. These two components fluctuate due to the external shocks or supply–demand self-adjustment, and tend to move towards the average level. In other works, high-frequency and low-frequency components fluctuate around dashed lines near zero, since the average of BDTI has to be separated as the residual. In brief, this implies that in the tanker shipping market there is the obvious mean reversion in the long run which is a common feature of time series. The consensus, therefore, is that freight rates are mean-reverting in the longer run as implied by the maritime economic theory (Adland and Cullinane, 2006; Tvedt, 2003). The potential for supply adjustment (new building and demolition) in a competitive market guarantees that extremely high or extremely low freight rates are not sustainable in the long run. Adland et al. (2008) concurred with Dixit and Pindyck (1994) in that it is difficult to detect long-run mean reversion particularly when using high-frequency data. However, it is convenient to examine the long-run mean reversion even if the daily data is used in our study. 4.2. Identifying the major scale To answer which component is of the major scale, Table 1 gives statistical measures in which the mean period is the value derived by dividing the total number of points by the number of peaks. The periods of high-frequency components of the BDTI and WTI are close to each other, 5.73 and 3.65 days, respectively, while periods of low-frequency components vary widely, 506.17 and 79.92 days, respectively. For the BDTI, the low-frequency component has a high correlation with the original time series and accounts for more than 50% of total variability. The high-frequency component and the residual impact the original tanker freight rates almost of the same extent but with dif￾ferent performances. The proportion of variability of high-frequency component is a little higher than that of the residual, still accounting for about 25% of total variability. All the three components show obvi￾ous correlations with the original BDTI, and taking correlation coeffi- cients into account, we can come to the conclusion that the low￾frequency component explains the highest proportion of the original BDTI. In other words, the low-frequency component determines the major scale of tanker freight rates. Meanwhile, high-frequency compo￾nent and residual also provide explanation of a large proportion. Differently, crude oil price is practically determined by the long￾term trend (that is, the residual), which accounts for more than 73% of observed price variability. Next, the low-frequency component has a mean period of about 80 days and accounts for about 25% of total variability, while its Pearson's γ reaches a high level of 0.71, meaning that a linear correlation exists. However, the high-frequency component just accounts for about 0.58% of total variability with a very low Pearson's coefficient. Thus, it is concluded that the long-term trend is the major scale for oil price compared with the second important scale, e.g., low￾frequency component. This feature has also been examined in Huang et al. (1998) and Zhang et al. (2008), and the residual is treated as the de￾terministic long-term behavior. To sum up, the low-frequency component is the major scale of the BDTI and the high-frequency and residual components are almost of equal significance. For the time series of the WTI, the residual is the major scale and low-frequency component is the second important scale, while the high-frequency component has hardly any role in determining the original WTI. More importantly, the residual of the BDTI first increases and then decreases after the turning point, while the residual of the WTI exhibits a trend of continued growth without any change in direction. 4.3. Analyzing the multiscale relevance between BDTI and WTI In this subsection, the relevance between the BDTI and the WTI is our focus. At first, the correlation coefficients between original WTI oil price and multiscale components of tanker freight rates are measured, as shown in Table 2. 4.3.1. Relevance between multiscale components Intuitively, the correlation between WTI and BDTI over a long time span is very low, with Pearson's coefficient of 0.065 and Kendall's coefficient of 0.0695. However, by dividing the original BDTI into three components, the behavior of correlation changes. Although the correla￾tion between the original WTI and high-frequency component of the BDTI is also very low, the low-frequency component and the residual are significantly correlated with the original WTI, in the opposite direction. The former is positive and the latter is negative. This suggests that it is necessary to decompose the original BDTI into different time– frequency components when exploring the relevance between the BDTI and WTI, because it can offer more correlation information. For a detailed analysis of the relevance, we further calculate the co￾efficients of correlation between multiscale components of BDTI and WTI (Table 3). The coefficients have characteristics similar to Table 1. For the BDTI, its high-frequency components show very low Table 3 Correlations of multiscale components between the BDTI and WTI. Correlations Pearson's γ Kendall's τ Components Highf of WTI Lowf of WTI Res. of WTI Highf of WTI Lowf of WTI Res. of WTI Highf of BDTI 0.00⁎ 0.10⁎ 0.07⁎ 0.00⁎ 0.03⁎ 0.06⁎ Lowf of BDTI −0.01⁎ 0.51⁎ 0.21⁎ −0.01⁎ 0.35⁎ 0.14⁎ Res. of BDTI −0.02⁎ −0.26⁎ −0.60⁎ −0.01⁎ −0.37⁎ −0.37⁎ ⁎ Correlation is significant at the 0.05 level (2-tailed). Table 2 Correlations between original WTI and multiscale components of the BDTI. Original BDTI Highf of BDTI Lowf of BDTI Res. of BDTI Pearson's γ 0.0655⁎ 0.0987⁎ 0.4170⁎ −0.5753⁎ Kendall's τ 0.0695⁎ 0.0504⁎ 0.3037⁎ −0.3311⁎ ⁎ Correlation is significant at the 0.05 level (2-tailed). 292 X. Sun et al. / Economic Modelling 42 (2014) 287–295

X.Sun et al Economic Modelling 42 (2014)287-295 293 100 Res.of BDTI Res.ofWTI 60 1400 40 1200, 1000. 0 800. 600 400- TTT7 TTTTTTTTTT 1998.08.032000.08.162002.09.012004.09.222007.04.122009.06.162011.08.08 Fig.6.Residual components extracted from the BDTI and WTI D BDTI Lighf-WTI Lighf BDTIRes-WTELRSAY BDTI Lighf BDTI Highf-WTI Res. BDTI Highf-WTILighf P BDTI Res.-WTI Highf BDTI Lighf-WTI Highf Period of high oil price Period of low oil price BDTI Highf-WTI Highf -0.8 -0.6 0.4 -0.2 0 02 0.4 0.6 0.8 Fig.7.Comparison of multiscale correlations between the BDTI and WTI in sub-periods. correlations with multiscale components of the WTI,and this applies to Pearson's coefficient reaching 0.51 and Kendall's coefficient being at a the WTl also.Therefore,this implies that the correlation between the relatively high level of 0.35.However,the second exists between resid- low-frequency components and the residual should be paid more atten- ual of the BDTI and the low-frequency component of the WTI in the tion.The highest correlation is between the two residuals of the BDTI viewpoint of Kendall's coefficient.Therefore,correlations between the and the WTI with negative Pearson's coefficient and Kendall's reaching two residuals and the two low-frequency components are further ana- -0.60 and-0.37,respectively.The second highest correlation exists lyzed in the following part. between the two low-frequency components,with the positive 4.3.2.Relevance in different periods As shown in Fig.6,the residual at first increased until the maximum point,the 1194th point (that is,18 June 2003).After the turning point, s00,000 the residual continuously decreased.It is obvious that the correlation structure changes before and after the turning point.Thus,we divided 450.000 the whole sample into two subsamples,where the first subsample is from the first to the 1194th point and the second subsample includes 400.000 all points from the 1195th to the end point. Additionally,oil price is low(not more than 40.00 dollar per barrel) 350.000 in the first subsample period,while it dramatically increases and fluctu- ates in the second period,as shown in Fig.1.In other words,the first period can be called the period of low oil price and the second can be 300.000 called the period of high oil price.Then,the correlations are calculated again for the two periods,and are depicted in Fig.7.We find an interest- 250,000- 19981999200020012002200320042005200620072008200920102011 ing phenomenon that the long-term correlation between the two residuals of the BDTI and WTI is extremely high,almost close to 1.00, Fig.8.Tanker fleet development of total world (as at year end-in Th.DWT). but in the totally opposite direction

correlations with multiscale components of the WTI, and this applies to the WTI also. Therefore, this implies that the correlation between the low-frequency components and the residual should be paid more atten￾tion. The highest correlation is between the two residuals of the BDTI and the WTI with negative Pearson's coefficient and Kendall's reaching −0.60 and −0.37, respectively. The second highest correlation exists between the two low-frequency components, with the positive Pearson's coefficient reaching 0.51 and Kendall's coefficient being at a relatively high level of 0.35. However, the second exists between resid￾ual of the BDTI and the low-frequency component of the WTI in the viewpoint of Kendall's coefficient. Therefore, correlations between the two residuals and the two low-frequency components are further ana￾lyzed in the following part. 4.3.2. Relevance in different periods As shown in Fig. 6, the residual at first increased until the maximum point, the 1194th point (that is, 18 June 2003). After the turning point, the residual continuously decreased. It is obvious that the correlation structure changes before and after the turning point. Thus, we divided the whole sample into two subsamples, where the first subsample is from the first to the 1194th point and the second subsample includes all points from the 1195th to the end point. Additionally, oil price is low (not more than 40.00 dollar per barrel) in the first subsample period, while it dramatically increases and fluctu￾ates in the second period, as shown in Fig. 1. In other words, the first period can be called the period of low oil price and the second can be called the period of high oil price. Then, the correlations are calculated again for the two periods, and are depicted in Fig. 7. We find an interest￾ing phenomenon that the long-term correlation between the two residuals of the BDTI and WTI is extremely high, almost close to 1.00, but in the totally opposite direction. 400 600 800 1000 1200 1400 0 20 40 60 80 100 Res.of BDTI Res.of WTI 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 Fig. 6. Residual components extracted from the BDTI and WTI. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 BDTI Highf - WTI Highf BDTI Lighf - WTI Highf BDTI Res. - WTI Highf BDTI Highf - WTI Lighf BDTI Highf - WTI Res. BDTI Lighf - WTI Res. BDTI Res. - WTI Lighf BDTI Lighf - WTI Lighf BDTI Res. - WTI Res. Period of high oil price Period of low oil price Fig. 7. Comparison of multiscale correlations between the BDTI and WTI in sub-periods. 250,000 300,000 350,000 400,000 450,000 500,000 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Fig. 8. Tanker fleet development of total world (as at year end — in Th. DWT). X. Sun et al. / Economic Modelling 42 (2014) 287–295 293

294 X.Sun et aL Economic Modelling 42 (2014)287-295 80 frequency component of the BDTI is smoother than that of the WTI, Lowf of BDTI -60 and exhibits an obvious fluctuation cycle with a periodicity of about 506 days. 40 In conclusion,the relevance between the BDTI and the WTl is mainly 20 accounted for by residual and low-frequency components.This implies that there are medium and long-term correlations between freight rates and oil prices.The BDTI is an index that reflects the trend and fluctua- tion of international tanker freight rates.In order to conduct a more in-depth analysis,tanker freight rates for all sizes of major crude oil shipping routes shown with the unit of dollar per barrel in Fig.10 are considered. According to OPEC's Annual Statistics Bulletin 2012,Middle East had more than 54%and Latin America about 23%of oil reserves of the world at the end of 2011.The routes from the Gulf to the West,from the Gulf to the East and from the Caribbean to US Atlantic Coast(USAC)cover oil -800 transportation from the above two major oil-producing regions to oil- 1998.08.032000.08.162002.09.012004.09.222007.04.122009.06.162011.08.08 consuming countries.The trend of the above freight rates is similar to Fig 9.Low-frequency components of the BDTI and WTL that of oil price.Specifically,the Caribbean/USAC as a regional market is correlated with oil price at a low level with a coefficient of 0.25.The Gulf/West and Gulf/East routes with longer shipping distance are more international than the Caribbean/USAC.Freight rates of the Gulf/ West route have the highest correlation with oil price and the next is During the period of low oil price,the long-term correlation is the Gulf/East route.The correlation coefficients of these two routes are positive while it is negative during the period of high oil price.One 0.62 and 0.58,respectively.Taking Fig.10 together with Fig.9,the possible explanation might be that tanker freight rates are not only performance of annual tanker freight rates is similar to that of the affected by costs that are mainly determined by oil price,but also influ- low-frequency components.Moreover,the correlations between oil enced by tanker supply and demand.As shown in Fig.8,the tanker fleet price and freight rates for major routes are close to those of low- was stable and it decreased a little during 1988 to 2002.According to the frequency components of BDTI and WTl:Pearson's coefficient is 0.68 statistics of OPEC,"the supply of tanker fleet recovered to the level of in the period of low oil price and 0.52 in the period of high oil price. 1998 in 2003,and after that the tanker fleet quickly increased until 2009,displaying high volatility during the period.The identification of 5.Conclusion and future work the year 2003 is in accord with analysis of the turning point in Fig.6. Oil price and tanker freight in the first period are mainly set accord- Uncertainty of tanker shipping market is correlated to volatility of ing to the basic economic law of supply and demand.Oil price changes the oil market,and this makes necessary to explore the inherent dy- around the equilibrium price due to the relatively stable supply and namic relationship between freight rates and oil prices.Taking the demand.Meanwhile,the tanker supply and demand are also relatively time-dependent features into account when modeling freight rates stable.Under the circumstances,an increase in oil price tends to this paper tries to investigate the dynamic relationship between tanker increase fuel cost and then pushes the tanker freight rate up.This freight rates and oil prices in the perspective of multiscale relevance, leads to a positive correlation.While in the second period,more and which is different from extant literature.Most importantly,it provides more non-economic factors affect the price and changes in freight a novel framework to investigate the inherent dynamic relationship be- rates,such as speculation,hedging and geopolitics,besides the law of tween two markets. supply and demand.Price rise has been the major characteristic of the Empirical results show that tanker freight rates and oil prices exhibit oil market because of the growing demand and limited supplies as oil different multiscale properties with economic meaning which can be is not a renewable resource.So oil price may move away from the identified as the long-term trend,medium-term pattern in low frequen- equilibrium price to a very large extent.In the meantime,although oil cy and short-term fluctuation in high frequency.Interestingly,it is price still affects fuel cost,it is no longer as important a factor as in the found that there is a turning point of relevance structure in June 2003. first period.Tanker freight rates are also influenced by other factors in which divided the whole sample into two sub-periods,high oil price pe- which new capacity plays an important role.This explains why most riod and low oil price period.Correlation between the two residuals of of the correlations in the second period are a little lower than in the the BDTI and WTI is extremely high and almost close to 1.00,but in to- first period.More and more newly built tankers are continuously put tally opposite direction in the two sub-periods.However,correlations into service because of the growing oil demand,and this can pull freight between medium-term patterns in low frequency are both high and rates down due to market competition. positive.This implies that it is necessary and rational to consider the dy- Also,Fig.9 shows that the second highest correlation is between namic relationship in multiscales under the relevance structure. low-frequency components which account for the medium-term In fact,the multiscale relevance between tanker freight rates and oil pattern of original BDTI and WTI.When the low-frequency component prices is our focus in the paper.In this context,the paper does not in- of oil price exhibits bigger fluctuations,low-frequency component of volve the following issues:the supply adjustment cycle,determinants the BDTI also experiences similar volatility.As mentioned above,the of the multiscale relevance,time frequency of the original data and fore- low-frequency component describes the structural pattern of original casting the freight rates when considering multiscale relevance.Inevita- time series.These two medium-term patterns show a similar trend, bly,our future work will center on these issues. for example,the fluctuation marked by the shadow.The low- Acknowledgments The authors gratefully acknowledge the financial support from National Natural Science Foundation of China (Nos.71003091, The data is available at http://www.opec.org/library// 71373009 and 71133005)the program of Youth Innovation Promotion interactive/current/FileZ/Main-Dateien/Section4html. Association supported by Chinese Academy of Sciences(CAS),and Key

During the period of low oil price, the long-term correlation is positive while it is negative during the period of high oil price. One possible explanation might be that tanker freight rates are not only affected by costs that are mainly determined by oil price, but also influ￾enced by tanker supply and demand. As shown in Fig. 8, the tanker fleet was stable and it decreased a little during 1988 to 2002. According to the statistics of OPEC,4 the supply of tanker fleet recovered to the level of 1998 in 2003, and after that the tanker fleet quickly increased until 2009, displaying high volatility during the period. The identification of the year 2003 is in accord with analysis of the turning point in Fig. 6. Oil price and tanker freight in the first period are mainly set accord￾ing to the basic economic law of supply and demand. Oil price changes around the equilibrium price due to the relatively stable supply and demand. Meanwhile, the tanker supply and demand are also relatively stable. Under the circumstances, an increase in oil price tends to increase fuel cost and then pushes the tanker freight rate up. This leads to a positive correlation. While in the second period, more and more non-economic factors affect the price and changes in freight rates, such as speculation, hedging and geopolitics, besides the law of supply and demand. Price rise has been the major characteristic of the oil market because of the growing demand and limited supplies as oil is not a renewable resource. So oil price may move away from the equilibrium price to a very large extent. In the meantime, although oil price still affects fuel cost, it is no longer as important a factor as in the first period. Tanker freight rates are also influenced by other factors in which new capacity plays an important role. This explains why most of the correlations in the second period are a little lower than in the first period. More and more newly built tankers are continuously put into service because of the growing oil demand, and this can pull freight rates down due to market competition. Also, Fig. 9 shows that the second highest correlation is between low-frequency components which account for the medium-term pattern of original BDTI and WTI. When the low-frequency component of oil price exhibits bigger fluctuations, low-frequency component of the BDTI also experiences similar volatility. As mentioned above, the low-frequency component describes the structural pattern of original time series. These two medium-term patterns show a similar trend, for example, the fluctuation marked by the shadow. The low￾frequency component of the BDTI is smoother than that of the WTI, and exhibits an obvious fluctuation cycle with a periodicity of about 506 days. In conclusion, the relevance between the BDTI and the WTI is mainly accounted for by residual and low-frequency components. This implies that there are medium and long-term correlations between freight rates and oil prices. The BDTI is an index that reflects the trend and fluctua￾tion of international tanker freight rates. In order to conduct a more in-depth analysis, tanker freight rates for all sizes of major crude oil shipping routes shown with the unit of dollar per barrel in Fig. 10 are considered. According to OPEC's Annual Statistics Bulletin 2012, Middle East had more than 54%, and Latin America about 23% of oil reserves of the world at the end of 2011. The routes from the Gulf to the West, from the Gulf to the East and from the Caribbean to US Atlantic Coast (USAC) cover oil transportation from the above two major oil-producing regions to oil￾consuming countries. The trend of the above freight rates is similar to that of oil price. Specifically, the Caribbean/USAC as a regional market is correlated with oil price at a low level with a coefficient of 0.25. The Gulf/West and Gulf/East routes with longer shipping distance are more international than the Caribbean/USAC. Freight rates of the Gulf/ West route have the highest correlation with oil price and the next is the Gulf/East route. The correlation coefficients of these two routes are 0.62 and 0.58, respectively. Taking Fig. 10 together with Fig. 9, the performance of annual tanker freight rates is similar to that of the low-frequency components. Moreover, the correlations between oil price and freight rates for major routes are close to those of low￾frequency components of BDTI and WTI: Pearson's coefficient is 0.68 in the period of low oil price and 0.52 in the period of high oil price. 5. Conclusion and future work Uncertainty of tanker shipping market is correlated to volatility of the oil market, and this makes necessary to explore the inherent dy￾namic relationship between freight rates and oil prices. Taking the time-dependent features into account when modeling freight rates, this paper tries to investigate the dynamic relationship between tanker freight rates and oil prices in the perspective of multiscale relevance, which is different from extant literature. Most importantly, it provides a novel framework to investigate the inherent dynamic relationship be￾tween two markets. Empirical results show that tanker freight rates and oil prices exhibit different multiscale properties with economic meaning which can be identified as the long-term trend, medium-term pattern in low frequen￾cy and short-term fluctuation in high frequency. Interestingly, it is found that there is a turning point of relevance structure in June 2003, which divided the whole sample into two sub-periods, high oil price pe￾riod and low oil price period. Correlation between the two residuals of the BDTI and WTI is extremely high and almost close to 1.00, but in to￾tally opposite direction in the two sub-periods. However, correlations between medium-term patterns in low frequency are both high and positive. This implies that it is necessary and rational to consider the dy￾namic relationship in multiscales under the relevance structure. In fact, the multiscale relevance between tanker freight rates and oil prices is our focus in the paper. In this context, the paper does not in￾volve the following issues: the supply adjustment cycle, determinants of the multiscale relevance, time frequency of the original data and fore￾casting the freight rates when considering multiscale relevance. Inevita￾bly, our future work will center on these issues. Acknowledgments The authors gratefully acknowledge the financial support from National Natural Science Foundation of China (Nos. 71003091, 71373009 and 71133005) the program of Youth Innovation Promotion Association supported by Chinese Academy of Sciences (CAS), and Key 4 The data is available at http://www.opec.org/library/Annual%20Statistical%20Bulletin/ interactive/current/FileZ/Main-Dateien/Section4.html. -800 -400 0 400 800 -40 -20 0 20 40 60 80 Lowf of BDTI Lowf of WTI 1998.08.03 2000.08.16 2002.09.01 2004.09.22 2007.04.12 2009.06.16 2011.08.08 Fig. 9. Low-frequency components of the BDTI and WTI. 294 X. Sun et al. / Economic Modelling 42 (2014) 287–295

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