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Recent studies suggested that shocks on volatility have long-lasting effects.This phenomenon is known in the empirical finance literature as long-range dependence behavior or long memory behavior(Charfeddine and Ajmi,2013).When the effects of volatility shocks decay slowly,long memory in volatility would occur. Significance is attached to the long memory feature,mainly for the sake of its accordance with the presence of nonlinear dependence between observations.Although long memory features have been discussed in many fields,including hydrology,Internet traffic,commodity market and energy future market(Barkoulas et al., 1998;Chen et al.,2006;Crato and Ray,2000;Elder and Jin,2007;Ohanissian et al.,2008;Panas,2001;Wang and Wu,2012),few researches focus on the long memory feature in freight rate market.As claimed by Yalama and Celik (2013),different financial markets and different sampling periods may present different characteristics of long-range correlation.Therefore,the long memory study focused on freight rate market is indispensable.In this paper,the Detrended Fluctuation Analysis(DFA)method is employed to study the long memory feature of freight rate volatility and the robustness of long-memory inference on daily freight rate index prediction.Compared with other methods which can be used in long memory analysis,such as Rescaled Range Method(R/S)and spectrum analysis method employed in the study of Kai et al.(Kai et al.,2008),an indisputable advantage of DFA is that it can detect the long-range correlations embedded in a non-stationary time series,without being influenced by spurious detection of apparent long-range correlations caused by external trends.The impact of seasonality has also been taken into account in the optimization of DFA,since literatures have shown that freight rate market is seasonal (Kavussanos.2001.2002). Additionally,a crucial issue that arises when analyzing the characteristic of long memory is that the existence of structural breaks can have influence on the long memory of freight rate volatility.In spite of the considerable researches that focus on long memory features of volatility,long memory studies on time series with structural breaks are still limited.The Iterated Cumulative Sum of Squares(ICSS)algorithm,which was developed by(Inclan and Tiao,1994),is proved to be one of the most popular and useful ways in studying the structural transition points of volatility (Aggarwal et al.,1999;Fernandez and Arago,2003;Malik,2003; Malik et al.,2005).Thus,ICSS method is adopted in order to detect structural break points in this paper. Studies on freight rate volatility as well as the long memory component and structural breaks have been thoroughly established by plentiful empirical studies(Baillie et al.,2007;Elder and Serletis,2008;Fernandez, 2010;Wang and Wu,2012).Nevertheless,tests for potential structural breaks and their impacts on the estimated fractional long memory parameter have been conducted in only a few studies(Arouri et al.,2012; Baillie and Morana,2009;Christensen,2010;Ozdemir et al.,2013).Moreover,DFA-based researches on long memory features in bulk freight market are still inadequate.Therefore,in this paper,we provide DFA results of Baltic Panamax Index(BPD),Baltic Supramax Index(BSI)and Baltic Capesize Index(BCD),which validate the long memory features in bulk freight rate market.The impact of seasonality has also been taken into account in the optimization of DFA. The paper is further organized as follows:Section 2 applies the DFA and ICSS model to analyze of freight rate volatility;Section 3 describes the data used in the long memory test;Section 4 demonstrates the analysis of long memory and structural break of historical data with DFA and ICSS method respectively;Section 5 summaries and concludes 33 Recent studies suggested that shocks on volatility have long-lasting effects. This phenomenon is known in the empirical finance literature as long-range dependence behavior or long memory behavior (Charfeddine and Ajmi, 2013). When the effects of volatility shocks decay slowly, long memory in volatility would occur. Significance is attached to the long memory feature, mainly for the sake of its accordance with the presence of nonlinear dependence between observations. Although long memory features have been discussed in many fields, including hydrology, Internet traffic, commodity market and energy future market (Barkoulas et al., 1998; Chen et al., 2006; Crato and Ray, 2000; Elder and Jin, 2007; Ohanissian et al., 2008; Panas, 2001; Wang and Wu, 2012), few researches focus on the long memory feature in freight rate market. As claimed by Yalama and Celik (2013), different financial markets and different sampling periods may present different characteristics of long-range correlation. Therefore, the long memory study focused on freight rate market is indispensable. In this paper, the Detrended Fluctuation Analysis (DFA) method is employed to study the long memory feature of freight rate volatility and the robustness of long-memory inference on daily freight rate index prediction. Compared with other methods which can be used in long memory analysis, such as Rescaled Range Method (R/S) and spectrum analysis method employed in the study of Kai et al.(Kai et al., 2008), an indisputable advantage of DFA is that it can detect the long-range correlations embedded in a non-stationary time series, without being influenced by spurious detection of apparent long-range correlations caused by external trends. The impact of seasonality has also been taken into account in the optimization of DFA , since literatures have shown that freight rate market is seasonal (Kavussanos, 2001, 2002). Additionally, a crucial issue that arises when analyzing the characteristic of long memory is that the existence of structural breaks can have influence on the long memory of freight rate volatility. In spite of the considerable researches that focus on long memory features of volatility, long memory studies on time series with structural breaks are still limited. The Iterated Cumulative Sum of Squares (ICSS) algorithm, which was developed by (Inclan and Tiao, 1994), is proved to be one of the most popular and useful ways in studying the structural transition points of volatility (Aggarwal et al., 1999; Fernández and Aragó, 2003; Malik, 2003; Malik et al., 2005). Thus, ICSS method is adopted in order to detect structural break points in this paper. Studies on freight rate volatility as well as the long memory component and structural breaks have been thoroughly established by plentiful empirical studies (Baillie et al., 2007; Elder and Serletis, 2008; Fernandez, 2010; Wang and Wu, 2012). Nevertheless, tests for potential structural breaks and their impacts on the estimated fractional long memory parameter have been conducted in only a few studies (Arouri et al., 2012; Baillie and Morana, 2009; Christensen, 2010; Ozdemir et al., 2013). Moreover, DFA-based researches on long memory features in bulk freight market are still inadequate. Therefore, in this paper, we provide DFA results of Baltic Panamax Index (BPI), Baltic Supramax Index (BSI) and Baltic Capesize Index (BCI), which validate the long memory features in bulk freight rate market. The impact of seasonality has also been taken into account in the optimization of DFA. The paper is further organized as follows: Section 2 applies the DFA and ICSS model to analyze of freight rate volatility; Section 3 describes the data used in the long memory test; Section 4 demonstrates the analysis of long memory and structural break of historical data with DFA and ICSS method respectively; Section 5 summaries and concludes
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