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). Internationally, 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 phenomenon 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 factors (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 complexity 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 ambiguous (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 relationship 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 reduction 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 relationship 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 components 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 components. 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 constructed in terms of low frequency, high frequency and residual, and accordingly, 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 component 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 different 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 diffusion 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 decomposition 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 conditions: (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 symmetric 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 function 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 varying 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, without 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 underlying product of New York Mercantile Exchange's oil futures contracts. 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 multiplications 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 benchmark 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 independent 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