Volatility Forecasting of Crude Oil Market: Which Structural Change Based GARCH Models have Better Performance?

• Author: Zhang, Yue-Jun

1. INTRODUCTION

   The price of crude oil is one of the most important global economic indicators and is monitored by policymakers, producers, consumers and financial-market participants (e.g., Mi et al., 2017; Shi and Variam, 2017; Zhang and Wang, 2019). It has been confirmed that oil prices have become increasingly volatile, exceeding the levels of volatility of other commodities, and are more susceptible to market disturbances (Charles and Darne, 2017). However, because crude oil has a large impact not only on the macroeconomy, but also on the countries that are heavily export dependent on energy commodities such as natural gas, oil and coal (Hamilton, 2009). Therefore, modeling and forecasting the volatility of crude oil prices has become a critical topic in the world wide, due to its great influence on portfolio allocation, option pricing, and risk measurement and so on (e.g., Kang and Yoon, 2013; Zhang and Zhang, 2018; Jawadi et al., 2019).

   Much research has been done to evaluate the forecasting performance of different volatility models, particularly the GARCH-type models, which consider the conditional heteroscedasticity of crude oil price volatility and can capture some other characteristics, such as time-variation, volatility clustering and asymmetry (e.g., Mohammadi and Su, 2010; Salisu and Fasanya, 2013; Wei et al., 2010) (1). However, the GARCH-type models generally assume a stable structure of parameters in the volatility process and ignore the structural changes in crude oil market. But the structural changes always occur due to the exposure of crude oil market to the periods of large price changes and a number of drastic shocks, such as the Gulf wars, the Asian crisis, and the US and global recessions. Diebold and Inoue (2001) confirm that the neglected structural changes may result in spurious long memory by the Monte Carlo simulation, and Elder and Serletis (2008) also confirm this statement. To depict the structural changes in volatility, some scholars have also tried to improve the volatility forecasting accuracy by taking regime switching into account (2) (e.g., Cai, 1994; Fong and See, 2002; Sanzo, 2018). For example, Fong and See (2002) employ a Markov regime switching approach allowing for GARCH-dynamics and structural changes in both mean and variance to model the conditional volatility of daily returns in crude oil futures market. They document that the regime switching model performs better than non-switching models. In brief, the emergency or external drastic shocks usually cause the presence of structural changes in crude oil price volatility and many relevant works have been conducted across the world to depict the structural changes in crude oil price volatility.

   However, the crude oil market proves a typical complex system, and with the accelerating financialization of crude oil markets, the reaction of crude oil prices to various unexpected events becomes increasingly sensitive (Zhang et al., 2017). As a result, crude oil price and return series usually show significant structural changes with various degrees and forms, caused by various events such as US "911" terrorist attacks in 2001, global financial crisis in 2008, and Libyan civil war in 2011 (e.g., Li and Thompson, 2010; Plante and Strickler, 2021). Are there obvious differences in the impact of different types of events on the crude oil price volatility? How can this difference be better characterized? There seems to be no answer in the existing research. In order to more intuitively reflect the conjecture, we try to use the product partition model (PPM) to calculate the posterior probability of crude oil price series at each time point. Figure 1 shows the posterior probability for a change point of WTI and Brent crude oil price returns. It is obvious that the probability values unevenly disperse from 0 to 1. Significantly, the probability values of nearly 100 observations are lower than 0.4, and they almost stay at the periods from 2000 to 2003 and from 2010 to 2013, which cover the US "911" terrorist attacks in 2001, the nuclear crisis in Iran in 2002, the Iraq war in 2003, and the Libyan civil war in 2011, and so on. Meanwhile, the probability values of nearly 90 observations are higher than 0.4, and they basically concentrate on the Asian financial crisis in 1998, the global financial crisis in 2008, and the U.S. shale oil revolution in 2014. These results in Figure 1 are interesting, i.e., different types of events occurring in crude oil market usually lead to structural changes in various degrees and forms. For instance, local geopolitical events or policy adjustments often lead to a slight degree of structural changes, while financial crises tend to cause significant structural changes. Phillips et al. (2017) and Chen and Huang (2018) also propose that structural changes may not be instantaneous, and the changes induced by policy switch, preference changes, technological progress and environmental issues usually exhibit graduality in the long term. Chen and Hong (2012) find the presence of smooth structural changes in the varying prices. Therefore, it is interesting and necessary to deeply explore the structural changes caused by different shocks in crude oil price volatility, so as to reduce the impact of structural changes on the accuracy of volatility forecasts.

   Nonetheless, when we focus on relevant research in the crude oil market, we find that most of existing methods can only identify the abrupt structural changes caused by strong external shocks, and they always regard structural breaks as being sharp, pure jumping and self-adjusting, but hardly recognize the smooth structural changes caused by the slow response to external shocks (e.g., Fang and See, 2002; Li and Enders, 2018) (3). However, in other financial markets, some relevant research has recognized that the flexible Fourier form (FFF) GARCH models, which combine the GARCH models with the flexible Fourier form, can capture various degrees and forms of structural changes in light of different external shocks, i.e., structural breaks and smooth structural changes (e.g., Becker, 2006; Teterin and Brooks, 2016) (4). Enders and Lee (2012) also point out that the notable features of the flexible Fourier form include not needing to assume that the number or time of structural breaks is known a priori and transforming the problem of estimating the number, form, time, and magnitudes of the breaks into incorporating the appropriate frequency components into the estimation equation. Therefore, it is necessary to apply the FFF-GARCH-type models considering smooth shift to crude oil price volatility modeling and forecasting, since they regard the structural break as a smooth process and take into account not only structural breaks but also smooth structural changes. And it is of critical importance for energy economists, energy policymakers and energy market practitioners to explore more effective ways in which one can depict and identify structural changes in crude oil price volatility. For this reason, this paper incorporates the smooth shift and regime switching, which separately regard structural changes as being smooth and sharp, and aims at judging whether the different models based on structural change can beat the GARCH models in terms of the ability to forecast crude oil price volatility.

   Specifically, this paper extends the existing literature in the following ways. First, it identifies the modification of Gallant's (1981) flexible Fourier form (Ender and Lee, 2012) to control the structural changes in crude oil price volatility, allowing the variance equation of GARCH models to be interrupted. By doing so, it builds the FFF-GARCH-type models to judge whether considering smooth shift can improve the forecasting performance of the GARCH-type models on crude oil price volatility. Second, to judge whether the forecasting ability of the standard GARCH model can also arise because of the incorporation of regime switching, this paper employs the MRS-GARCH model to allow the parameter to vary across different regimes and take into account the existence of structural changes. Finally, it uses the rolling forecasting method to carry out the one-step ahead and multiple-step ahead volatility forecasting of crude oil market and apply various loss functions, Diebold-Mariano test and portfolio performance as the criteria for evaluating the forecasting performance.

   The contribution of this paper mainly includes the following three aspects: (1) Different from previous relevant studies, which usually regard the structural change as a sharp process, this paper regards the structural change as a smooth process, and builds the FFF-GARCH-type models incorporating the smooth shift into GARCH-type models. This new approach provides a novel perspective concerning the description of structural change in crude oil market. (2) Previous studies usually choose one method to depict or ignore possible structural changes in crude oil price volatility, but this paper further compares the volatility forecasts obtained by incorporating smooth shift and regime switching into the GARCH-type models, and confirms that the former one is significantly superior. This finding can help market participants and policy makers forecast crude oil price volatility more accurately, and provide important references concerning monitoring and avoiding extreme risks in crude oil market. (3) This paper uses the forecasting results of the FFF-GARCH-type models to construct different portfolio strategies, and finds that the new models can not only improve the forecasting performance of the GARCH-type models, but also increase their economic value.

   The remainder of this paper is organized as follows. Section 2 presents relevant literature review. Section 3 briefly describes the models. Section 4 provides the data, and Section 5 presents the empirical results. Section 6 concludes the paper.

2. METH...