Forecasting the volatility of crude oil futures using high-frequency data: further evidence

We forecast the realized volatility of crude oil futures market using the heterogeneous autoregressive model for realized volatility and its various extensions. Out-of-sample findings indicate that the inclusion of jumps does not improve the forecasting accuracy of the volatility models, whereas the “leverage effect” pertaining to the difference between positive and negative realized semi-variances can significantly improve the forecasting accuracy in predicting the short- and medium-term volatility. However, the signed jump variations and its decomposition couldn’t significantly enhance the models’ forecasting accuracy on the long-term volatility.     

Forecasting the realized volatility: the role of jumps

This article investigates the role of jump components dependent on the ABD-LM jump test in forecasting volatility. Our out-of-sample forecasting results show that compared with the ABD-LM jump component, its decomposition forms based on signed returns can significantly improve the models’ forecasting performance and our findings have important implications for investors and policymakers.     

Evaluating and improving GARCH-based volatility forecasts with range-based estimators

This article investigates the feasibility of using range-based estimators to evaluate and improve Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based volatility forecasts due to their computational simplicity and readily availability. The empirical results show that daily range-based estimators are sound alternatives for true volatility proxies when using Superior Predictive Ability (SPA) test of Hansen (2005) to assess GARCH-based volatility forecasts. In addition, the inclusion of the range-based estimator of Garman and Klass (1980) can significantly improve the forecasting performance of GARCH-t model.     

Forecasting realized volatility of crude oil futures with equity market uncertainty

This paper examines whether the equity market uncertainty (EMU) index contains incremental information for forecasting the realized volatility of crude oil futures. We use 5-min high-frequency transaction data for WTI crude oil futures and develop six heterogeneous autoregressive (HAR) models based on classical HAR-type models. The empirical results suggest that EMU contains more incremental information than the economic policy uncertainty (EPU) for forecasting the realized volatility of crude oil futures. More importantly, we argue that EMU is a non negligible additional predictive variable that can significantly improve the 1-day ahead predictive accuracy of all six HAR-type models, and improve the 1-week ahead forecasting performance of the HAR-RV, HAR-RV-J, HAR-RSV, HAR-RV-SJ models. These findings highlight a strong short-term and a weak mid-term predictive ability of EMU in the crude oil futures market.     

Forecasting the realized volatility in the Chinese stock market: further evidence

In this study, the impact of noise and jump on the forecasting ability of volatility models with high-frequency data is investigated. A signed jump variation is added as an additional explanatory variable in the volatility equation according to the sign of return. These forecasting performances of models with jumps are compared with those without jumps. Being applied to the Chinese stock market, we find that the jump variation has a significant in-sample predictive power to volatility and the predictive power of the negative one is greater than the positive one. Furthermore, out-of-sample evidence based on the fresh model confidence set (MCS) test indicates that the incorporation of singed jumps in volatility models can significantly improve their forecasting ability. In particular, among the realized variance (RV)-based volatility models and generalized autoregressive conditional heteroscedasticity (GARCH) class models, the heterogeneous autoregressive model of realized volatility (HAR-RV) model with the jump test and a decomposed signed jump variation have better out-of-sample forecasting performance. Finally, the use of the decomposed signed jump variations in predictive regressions can improve the economic value of realized volatility forecasts.     

Forecasting volatility in the Indian equity market using return and range-based models

In this article, we assess the time-varying volatility of the National Stock Exchange in the Indian equity market using unconditional estimators and asymmetric conditional econometric models. The volatility estimate and forecast is computed from the interday return and intraday range-based data of the exchange’s flagship index, CNX NIFTY, for the time period spanning 1 January 2009 through 31 December 2013. These are our findings: First, we determine that the time-varying volatility of the index is asymmetric with qualities of stationarity and leptokurtic distribution. Second, the one-step-ahead volatility forecast derived from the univariate time series parameters through the GJR-GARCH ?????process indicates that the model evaluation criteria of the autoregressive process tends towards range-based models vis-à-vis a return-based model. The validity of this methodology is further analysed with the superior predictive ability test, the outcome of which supports the use of range-based conditional models. Finally, among the evaluated range-based model variants, the model confidence set procedure favours the Yang–Zhang estimator as being better suited to forecast the exchange’s volatility than the ones by Parkinson, Garman–Klass and Rogers–Satchell.     

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

金融资产收益率波动预测——基于我国股票市场跳跃行为研究

金融资产收益率波动是资产定价和金融风险管理的核心部分,而跳跃是收益率波动中的重要组成部分。基于修正Z-检验,本文检测识别我国股市波动中跳跃行为,并且研究了跳跃的时序特征,统计结果表明,在市场大波动时期,和连续成份相比,跳跃对于波动率具有极其重要的贡献。建立包含跳跃的已实现波动率非齐次自回归模型,在波动模型中纳入滞后绝对日收益率和杠杆效应预测股指收益率波动。实证分析结果显示,对于短期的波动预测,包含跳跃和两种影响因素的波动模型表现最好,然而对于提前1月的长期预测,跳跃和连续波动成份分离模型预测明显优于其它模型,这些事实说明跳跃对股指波动率预测具有重要的影响,好坏消息对波动率非对称性具有短期显著影响,而对长期水平的波动率预测影响不显著。     

Volatility forecasting: long memory,regime switching and heteroscedasticity

In this article, we account for the first time for long memory, regime switching and the conditional time-varying volatility of volatility (heteroscedasticity) to model and forecast market volatility using the heterogeneous autoregressive model of realized volatility (HAR-RV) and its extensions. We present several interesting and notable findings. First, existing models exhibit significant nonlinearity and clustering, which provide empirical evidence on the benefit of introducing regime switching and heteroscedasticity. Second, out-of-sample results indicate that combining regime switching and heteroscedasticity can substantially improve predictive power from a statistical viewpoint. More specifically, our proposed models generally exhibit higher forecasting accuracy. Third, these results are widely consistent across a variety of robustness tests such as different forecasting windows, forecasting models, realized measures, and stock markets. Consequently, this study sheds new light on forecasting future volatility.     

Realized volatility transmission: The role of jumps and leverage effects

This paper is the first to employ a multivariate extension of the LHAR–CJ model for realized volatility of Corsi and Renó (2012) considering continuous and jump volatility components and leverage effects. The model is applied to financial (S&P 500), commodity (WTI crude oil) and forex (US$/EUR) intraday futures data and allows new insights in the transmission mechanisms among these markets. Besides significant leverage effects, we find that the jump components of all considered assets do not contain incremental information for the one-step ahead realized volatility. The volatility of S&P 500 and US$/EUR exchange rate futures exhibits significant spillovers to the realized volatility of WTI. Moreover, decreasing equity prices appear to increase volatility in other markets, while strengthening of the US$ seems to calm down the crude oil market.     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

On the predictive power of ARJI volatility forecasts for Bitcoin

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.     

ALLOWING FOR JUMP MEASUREMENTS IN VOLATILITY: A HIGH‐FREQUENCY FINANCIAL DATA ANALYSIS OF INDIVIDUAL STOCKS

Following recent advances in the non‐parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyse the distributional properties of the jump measures vis‐à‐vis the corresponding realized volatility ones, and compare them to those of aggregate US market index series. We also demonstrate important gains in the forecasting accuracy of high‐frequency volatility models.     

Modeling the volatility of futures return in rubber and oil—A Copula-based GARCH model approach

This paper attempts to make use of a Copula-based GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) Model to find out the relationships between the volatility of rubber futures returns in the Agricultural Futures Exchange of Thailand (AFET) and other four main markets, namely, the volatility of rubber futures returns in the Singapore Commodity Exchange (SICOM), the volatility of rubber futures returns, crude oil returns, and gas oil returns in the Tokyo Commodity Exchange (TOCOM). The results illustrate that the Student-t dependence only shows better explanatory power than the Gaussian dependence structure and the persistence pertaining to the dependence structure between rubber futures returns in AFET and oil futures returns, namely, crude oil futures returns and gas oil futures returns in TOCOM. Whereas, the Gaussian dependence shows better explanatory ability between rubber futures returns in AFET and other rubber futures returns, namely, the volatility of rubber futures in SICOM and TOCOM. For the multivariate Copula model, all the parameters between AFET and other variables are significant. Based on these results, with the liberalization of agricultural trade and the withdrawal of government support to agricultural producers, there is in many countries a new need for price discovery and even physical trading mechanisms, a need that can often be met by commodity futures exchanges. Hence, this paper recommends that the government supports the hedge mutual funds that can be invested in every commodities futures exchange in the world. It can also put the funds together that will contribute farmers to invest in each commodities futures market.     

Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.     

A study of Shanghai fuel oil futures price volatility based on high frequency data: Long-range dependence,modeling and forecasting

In existing researches, the investigations of oil price volatility are always performed based on daily data and squared daily return is always taken as the proxy of actual volatility. However, it is widely accepted that the popular realized volatility (RV) based on high frequency data is a more robust measure of actual volatility than squared return. Due to this motivation, we investigate dynamics of daily volatility of Shanghai fuel oil futures prices employing 5-minute high frequency data. First, using a nonparametric method, we find that RV displays strong long-range dependence and recent financial crisis can cause a lower degree of long-range dependence. Second, we model daily volatility using RV models and GARCH-class models. Our results indicate that RV models for intraday data overwhelmingly outperform GARCH-class models for daily data in forecasting fuel oil price volatility, regardless the proxy of actual volatility. Finally, we investigate the major source of such volatile prices and found that trader activity has major contribution to fierce variations of fuel oil prices.     

Which types of commodity price information are more useful for predicting US stock market volatility?

This study aims to investigate which types of commodity price information are more useful for predicting US stock market realized volatility (RV) in a data-rich word. The standard predictive regression framework and monthly RV data are used to explore the RV predictability of commodity futures for the next-month RV on S&P 500 spot index. We utilize principal component analysis (PCA) and factor analysis (FA) to extract the common factors for each type and all types of commodity futures. Our results indicate that the futures volatility information of grains and softs has a significant predictive ability in forecasting the RV of the S&P 500. In addition, the FA method can yield better forecasts than the PCA and average methods in most cases. Further analysis shows that the volatility information of grains and softs exhibits higher informativeness during recessions and pre-crises. Finally, the forecasts of the five combination methods and different out-of-sample periods confirm our results are robust.     

Linear time-varying regression with a DCC-GARCH model for volatility

This article provides a new linear state space model with time-varying parameters for forecasting financial volatility. The volatility estimates obtained from the model by using the US stock market data almost exactly match the realized volatility. We further compare our model with traditional volatility models in the ex post volatility forecast evaluations. In particular, we use the superior predictive ability and the reality check for data snooping. Evidence can be found supporting that our simple but powerful regression model provides superior forecasts for volatility.     

A new generalized volatility proxy via the stochastic volatility model

This article proposes power transformation of absolute returns as a new proxy of latent volatility in the stochastic model. We generalize absolute returns as a proxy for volatility in that we place no restriction on the power of absolute returns. An empirical investigation on the bias, mean square error and relative bias is carried out for the proposed proxy. Simulation results show that the new estimator exhibiting negligible bias appears to be more efficient than the unbiased estimator with high variance.     

Can GARCH-class models capture long memory in WTI crude oil markets?

This paper investigates the issue whether GARCH-type models can well capture the long memory widely existed in the volatility of WTI crude oil returns. In this frame, we model the volatility of spot and futures returns employing several GARCH-class models. Then, using two non-parametric methods, detrended fluctuation analysis (DFA) and rescaled range analysis (R/S), we compare the long memory properties of conditional volatility series obtained from GARCH-class models to that of actual volatility series. Our results show that GARCH-class models can well capture the long memory properties for the time scale larger than a year. However, for the time scale smaller than a year, the GARCH-class models are misspecified.