Volatility forecasting in the Bitcoin market: A new proposed measure based on the VS-ACARR approach

This paper proposes a new volatility-spillover-asymmetric conditional autoregressive range (VS-ACARR) approach that takes into account the intraday information, the volatility spillover from crude oil as well as the volatility asymmetry (leverage effect) to model/forecast Bitcoin volatility (price range). An empirical application to Bitcoin and crude oil (WTI) price ranges shows the existence of strong volatility spillover from crude oil to the Bitcoin market and a weak leverage effect in the Bitcoin market. The VS-ACARR model yields higher forecasting accuracy than the GARCH, CARR, and VS-CARR models regarding out-of-sample forecast performance, suggesting that accounting for the volatility spillover and asymmetry can significantly improve the forecasting accuracy of Bitcoin volatility. The superior forecast performance of the VS-ACARR model is robust to alternative out-of-sample forecast windows. Our findings highlight the importance of accommodating intraday information, spillover from crude oil, and volatility asymmetry in forecasting Bitcoin volatility.     

Time-varying risk aversion and renminbi exchange rate volatility: Evidence from CARR-MIDAS model

In this paper, we investigate the relation between time-varying risk aversion and renminbi exchange rate volatility using the conditional autoregressive range-mixed-data sampling (CARR-MIDAS) model. The CARR-MIDAS model is a range-based volatility model, which exploits intraday information regarding the intraday trajectory of the price. Moreover, the model features a MIDAS structure allowing for time-varying risk aversion to drive the long-run volatility dynamics. Our empirical results show that time-varying risk aversion has a significantly negative effect on the long-run volatility of renminbi exchange rate. Moreover, we observe that both intraday ranges and time-varying risk aversion contain important information for forecasting renminbi exchange rate volatility. The range-based CARR-MIDAS model incorporating time-varying risk aversion provides more accurate out-of-sample forecasts of renminbi exchange rate volatility compared to a variety of competing models, including the return-based GARCH, GARCH-MIDAS and GARCH-MIDAS incorporating time-varying risk aversion as well as range-based CARR, CARR-MIDAS and heterogeneous autoregressive (HAR), for forecast horizons of 1 day up to 3 months. This result is robust to alternative risk aversion measure, alternative MIDAS lags as well as alternative out-of-sample periods. Overall, our findings highlight the value of incorporating intraday information and time-varying risk aversion for forecasting the renminbi exchange rate volatility.     

Forecasting VIX using two-component realized EGARCH model

In this paper, we propose the two-component realized EGARCH (REGARCH-2C) model, which accommodates the high-frequency information and the long memory volatility through the realized measure of volatility and the component volatility structure, to forecast VIX. We obtain the risk-neutral dynamics of the REGARCH-2C model and derive the corresponding model-implied VIX formula. The parameter estimates of the REGARCH-2C model are obtained via the joint maximum likelihood estimation using observations on the returns, realized measure and VIX. Our empirical results demonstrate that the proposed REGARCH-2C model provides more accurate VIX forecasts compared to a variety of competing models, including the GARCH, GJR-GARCH, nonlinear GARCH, Heston–Nandi GARCH, EGARCH, REGARCH and two two-component GARCH models. This result is found to be robust to alternative realized measure. Our empirical evidence highlights the importance of incorporating the realized measure as well as the component volatility structure for VIX forecasting.     

Outlier Detection in the Lognormal Logarithmic Conditional Autoregressive Range Model

An outlier detection procedure in the lognormal logarithmic conditional autoregressive range (lognormal Log‐CARR) model is proposed. The proposed test statistic is demonstrated to be well‐sized and to have good power using Monte Carlo simulations. Furthermore, the outlier detection procedure suffers less from the masking effect caused by multiple outliers. The results of an empirical investigation show that the proposed method can effectively detect volatility outliers and improve forecasting accuracy.     

Forecasting crude oil price volatility

We use high-frequency intra-day realized volatility data to evaluate the relative forecasting performances of various models that are used commonly for forecasting the volatility of crude oil daily spot returns at multiple horizons. These models include the RiskMetrics, GARCH, asymmetric GARCH, fractional integrated GARCH and Markov switching GARCH models. We begin by implementing Carrasco, Hu, and Ploberger’s (2014) test for regime switching in the mean and variance of the GARCH(1, 1), and find overwhelming support for regime switching. We then perform a comprehensive out-of-sample forecasting performance evaluation using a battery of tests. We find that, under the MSE and QLIKE loss functions: (i) models with a Student’s t innovation are favored over those with a normal innovation; (ii) RiskMetrics and GARCH(1, 1) have good predictive accuracies at short forecast horizons, whereas EGARCH(1, 1) yields the most accurate forecasts at medium horizons; and (iii) the Markov switching GARCH shows a superior predictive accuracy at long horizons. These results are established by computing the equal predictive ability test of Diebold and Mariano (1995) and West (1996) and the model confidence set of Hansen, Lunde, and Nason (2011) over the entire evaluation sample. In addition, a comparison of the MSPE ratios computed using a rolling window suggests that the Markov switching GARCH model is better at predicting the volatility during periods of turmoil.     

How does inter-industry spillover improve the performance of volatility forecasting?

This study aims to investigate whether introducing inter-industry spillover information into the GARCH-MIDAS model improves out-of-sample forecasting attempts. We explore the transmission of volatility across sectors, as well as the reliance on inter-industry business links. Our findings demonstrate strong cross-industry volatility spillovers that are related to the degree of the industry-to-industry trading linkage. We compare the out-of-sample volatility forecasting performance of the spillovers-information-incorporated GARCH-MIDAS model with that of the traditional GARCH model. The empirical results show that the GARCH-MIDAS model outperforms traditional GARCH models. Notably, we discover that good (bad) news is always transferred from the back end of the production process to the front end, meaning that economic growth (decline) is driven by consumption expansion (shrinkage).     

Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators

This study employs the realized GARCH (RGARCH) model to estimate the volatility of Bitcoin returns and measure the benefits of various scaled realized measures in forecasting volatility. Empirical results show that considerable price jumps occurred in the Bitcoin market, suggesting that a jump-robust realized measure is crucial to estimate Bitcoin volatility. The RGARCH model, especially the one with tri-power variation, outperforms the standard GARCH model. Additionally, the RGARCH model with jump-robust realized measures can provide steady forecasting performance. This study is timely given that the CME may release a Bitcoin option product and our results are relevant to option pricing     

Open interest,volume, and volatility: evidence from Taiwan futures markets

This paper examines the relationships amongst volatility, total trading volume (TVOL) and total open interest (TOI) for three Taiwan stock index futures markets as well as the role of the latter two variables in the dynamics of GARCH modeling and forecasting. From both ex-post and ex-ante perspectives, we study this issue by using the VAR model and augmented GARCH-type models, respectively. For the GARCH-type models, we employ both symmetric and asymmetric models augmented with lagged logs in TOI and/or TVOL. We find that whether addition of these two variables helps the basic GARCH models predict future volatility depends upon the sample period examined for all three sets of futures. Nonetheless, the best three models for out-of-sample volatility forecasting in the MSE sense are generally the augmented models for all sub-intervals and all three futures contracts.     

Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.     

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting,incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.     

A semiparametric GARCH model for foreign exchange volatility

A semiparametric extension of the GJR model (Glosten et al., 1993. Journal of Finance 48, 1779–1801) is proposed for the volatility of foreign exchange returns. Under reasonable assumptions, asymptotic normal distributions are established for the estimators of the model, corroborated by simulation results. When applied to the Deutsche Mark/US Dollar and the Deutsche Mark/British Pound daily returns data, the semiparametric volatility model outperforms the GJR model as well as the more commonly used GARCH(1,1) model in terms of goodness-of-fit, and forecasting, by correcting overgrowth in volatility.     

Modelling the conditional volatility of commodity index futures as a regime switching process

Commodity index futures offer a versatile tool for gaining different forms of exposure to commodity markets. Volatility is a critical input in many of these applications. This paper examines issues in modelling the conditional variance of futures returns based on the Goldman Sachs Commodity Index (GSCI). Given that commodity markets tend to be ‘choppy’ (Webb, 1987 ), a general econometric model is proposed that allows for abrupt changes or regime shifts in volatility, transition probabilities which vary explicitly with observable fundamentals such as the basis, GARCH dynamics, seasonal variations and conditional leptokurtosis. The model is applied to daily futures returns on the GSCI over 1992–1997. The results show clear evidence of regime shifts in conditional mean and volatility. Once regime shifts are accounted for, GARCH effects are minimal. Consistent with the theory of storage, returns are more likely to switch to the high‐variance state when the basis is negative than when the basis is positive. The regime switching model also performs well in forecasting the daily volatility compared to standard GARCH models without regime switches. The model should be of interest to sophisticated traders who base their trading strategies on short‐term volatility movements, managed commodity funds interested in hedging an underlying diversified portfolio of commodities and investors of options and other derivatives tied to GSCI futures contracts. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting stock price volatility: New evidence from the GARCH-MIDAS model

This paper introduces a combination of asymmetry and extreme volatility effects in order to build superior extensions of the GARCH-MIDAS model for modeling and forecasting the stock volatility. Our in-sample results clearly verify that extreme shocks have a significant impact on the stock volatility and that the volatility can be influenced more by the asymmetry effect than by the extreme volatility effect in both the long and short term. Out-of-sample results with several robustness checks demonstrate that our proposed models can achieve better performances in forecasting the volatility. Furthermore, the improvement in predictive ability is attributed more strongly to the introduction of asymmetry and extreme volatility effects for the short-term volatility component.     

Forecasting the realized volatility of Energy Stock Market: A multimodel comparison

The realized volatility forecasting of energy sector stocks facilitates the establishment of corresponding risk warning mechanisms and investor decisions. In this paper, we collected two different energy sector indices and used different methods, namely principal component analysis (PCA) and sparse principal component analysis (SPCA), to extract features, and combined LSTM and GRU to construct 12 different models. The results show that the SPCA-LSTM model we constructed has the best forecasting performance in the realized volatility forecasting of energy indices, and SPCA has better forecasting results than PCA in the feature extraction stage. The results of the robustness test indicate that our results are robust.     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

Exchange rates and oil prices: A multivariate stochastic volatility analysis

This paper uses the multivariate stochastic volatility (MSV) and the multivariate GARCH (MGARCH) models to investigate the volatility interactions between the oil market and the foreign exchange (FX) market, in an attempt to extract information intertwined in the two for better volatility forecast. Our analysis takes into account structural breaks in the data. We find that when the markets are relatively calm (before the 2008 crisis), both oil and FX markets respond to shocks simultaneously and therefore no interaction is detected in daily data. However, during turbulent time, there is bi-directional volatility interaction between the two. In other words, innovations that hit one market also have some impact on the other at a later date and thus using such a dependence significantly improves the forecasting power of volatility models. The MSV models outperform others in fitting the data and forecasting exchange rate volatility. However, the MGARCH models do better job in forecasting oil volatility.     

Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling and forecasting of stock index volatility with APARCH models under ordered restriction

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student's t and skewed Student's t‐distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron) tests, co‐integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500 daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student's t‐distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.     

MULTIVARIATE VOLATILITY MODELING OF ELECTRICITY FUTURES

We model the dynamic volatility and correlation structure of electricity futures of the European Energy Exchange index. We use a new multiplicative dynamic conditional correlation (mDCC) model to separate long‐run from short‐run components. We allow for smooth changes in the unconditional volatilities and correlations through a multiplicative component that we estimate nonparametrically. For the short‐run dynamics, we use a GJR‐GARCH model for the conditional variances and augmented DCC models for the conditional correlations. We also introduce exogenous variables to account for congestion and delivery date effects in short‐term conditional variances. We find different correlation dynamics for long‐ and short‐term contracts and the new model achieves higher forecasting performance compared \to a standard DCC model. Copyright © 2012 John Wiley & Sons, Ltd.     

Two are better than one: Volatility forecasting using multiplicative component GARCH-MIDAS models

We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of generalized autoregressive conditional heteroskedasticity–mixed-data sampling (GARCH-MIDAS) models suggested in Engle, Ghysels, and Sohn (Review of Economics and Statistics, 2013, 95, 776–797). In those models volatility is decomposed into a short-term GARCH component and a long-term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the R² of a Mincer–Zarnowitz regression and evaluate the QMLE and forecast performance of these models in a Monte Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH-MIDAS models with a wide range of competitor models such as HAR (heterogeneous autoregression), realized GARCH, HEAVY (high-frequency-based volatility) and Markov-switching GARCH. Our results show that the GARCH-MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of 2 and 3 months ahead.