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