Forecasting the Chinese stock market volatility with international market volatilities: The role of regime switching

The purpose of this paper is to investigate the role of regime switching in the prediction of the Chinese stock market volatility with international market volatilities. Our work is based on the heterogeneous autoregressive (HAR) model and we further extend this simple benchmark model by incorporating an individual volatility measure from 27 international stock markets. The in-sample estimation results show that the transition probabilities are significant and the high volatility regime exhibits substantially higher volatility level than the low volatility regime. The out-of-sample forecasting results based on the Diebold-Mariano (DM) test suggest that the regime switching models consistently outperform their original counterparts with respect to not only the HAR and its extended models but also the five used combination approaches. In addition to point accuracy, the regime switching models also exhibit substantially higher directional accuracy. Furthermore, compared to time-varying parameter, Markov regime switching is found to be a more efficient way to process the volatility information in the changing world. Our results are also robust to alternative evaluation methods, various loss functions, alternative volatility estimators, various sample periods, and various settings of Markov regime switching. Finally, we provide an extension of forecasting aggregate market volatility on monthly frequency and observe mixed results.     

Applications of machine learning for corporate bond yield spread forecasting

This article considers nine different predictive techniques, including state-of-the-art machine learning methods for forecasting corporate bond yield spreads with other input variables. We examine each method’s out-of-sample forecasting performance using two different forecast horizons: (1) the in-sample dataset over 2003–2007 is used for one-year-ahead and two-year-ahead forecasts of non-callable corporate bond yield spreads; and (2) the in-sample dataset over 2003–2008 is considered to forecast the yield spreads in 2009. Evaluations of forecasting accuracy have shown that neural network forecasts are superior to the other methods considered here in both the short and longer horizon. Furthermore, we visualize the determinants of yield spreads and find that a firm’s equity volatility is a critical factor in yield spreads.     

Does the Macroeconomy Predict UK Asset Returns in a Nonlinear Fashion? Comprehensive Out‐of‐Sample Evidence

We perform a comprehensive examination of the recursive, comparative predictive performance of linear and nonlinear models for UK stock and bond returns. We estimate Markov switching, threshold autoregressive (TAR) and smooth transition autoregressive (STR) regime switching models and a range of linear specifications including models with GARCH type specifications. Results demonstrate UK asset returns require nonlinear dynamics to be modelled with strong evidence in favour of Markov switching frameworks. Our results appear robust to the choice of sample period, changes in loss functions and to the methodology employed to test for equal predictive accuracy. The key findings extend to a similar sample of US data.     

Modelling Regime‐Specific Stock Price Volatility*

Single‐state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state‐dependent behaviour of volatility nor explain why the equity index skew persists into long‐dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state‐dependent leverage effect to NM‐GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time‐varying volatility risk premia. An empirical study on European equity indices identifies two‐state asymmetric NM‐GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean‐reversion and leverage effects during crash markets are quite different from those in the stable regime.     

Forecasting global equity market volatilities

Motivated by a common belief that the international stock market volatilities are synonymous with information flow, this paper proposes a parsimonious way to combine multiple market information flows and assess whether cross-national volatility flows contain important information content that can improve the accuracy of international volatility forecasting. We concentrate on realized volatilities (RV) derived from the intra-day prices of 22 international stock markets, and employ the heterogeneous autoregressive (HAR) framework, along with two common diffusion indices that are constructed based on the simple mean and first principal component (PC) of the 22 stock market RVs, to forecast future volatilities of each market for 1-day, 1-week, and 1-month ahead. We provide strong evidence that the use of the cross-national information reflected by the simple and parsimonious common indices enhances the predictive accuracy of international volatilities at all forecasting horizons. Alternative volatility measures, estimation window sizes, and forecasting evaluation tests confirm the robustness of our results. Finally, our strategy of constructing common diffusion indices is also feasible for international market jumps.     

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.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

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.     

Adding dummy variables: A simple approach for improved volatility forecasting in electricity market

This study used dummy variables to measure the influence of day-of-the-week effects and structural breaks on volatility. Considering day-of-the-week effects, structural breaks, or both, we propose three classes of HAR models to forecast electricity volatility based on existing HAR models. The estimation results of the models showed that day-of-the-week effects only improve the fitting ability of HAR models for electricity volatility forecasting at the daily horizon, whereas structural breaks can improve the in-sample performance of HAR models when forecasting electricity volatility at daily, weekly, and monthly horizons. The out-of-sample analysis indicated that both day-of-the-week effects and structural breaks contain additional ex ante information for predicting electricity volatility, and in most cases, dummy variables used to measure structural breaks contain more out-of-sample predictive information than those used to measure day-of-the-week effects. The out-of-sample results were robust across three different methods. More importantly, we argue that adding dummy variables to measure day-of-the-week effects and structural breaks can improve the performance of most other existing HAR models for volatility forecasting in the electricity market.     

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.     

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.     

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.     

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.     

How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches

This paper examines the dynamic relationship between firm-level return volatility and public news sentiment. By using the new RavenPack News Analytics ⿿ Dow Jones Edition database that captures over 1200 types of firm-specific and macroeconomic news releases and their sentiment scores at high frequencies, we investigate the circumstances in which public news sentiment is related to the intraday volatility of the constituent stocks in the Dow Jones Composite Average (DJN 65). Two different conditionally heteroskedastic models are employed: the Fractionally Integrated Generalized Autoregressive Conditionally Heteroskedastic (FIGARCH) and the two-state Markov Regime-Switching GARCH (RS-GARCH) models. For most of the DJN 65 stocks, our results confirm the significant impact of firm-specific news sentiment on intraday volatility persistence, even after controlling for the potential effects of macroeconomic news. Compared with macroeconomic news sentiment, firm-specific news sentiment apparently accounts for a greater proportion of overall volatility persistence. Moreover, negative news has a greater impact on volatility than positive news. Furthermore, the results from the RS-GARCH model indicate that news sentiment accounts for a greater proportion of volatility persistence in the high-volatility regime (turbulent state) than in the low-volatility regime (calm state). In-sample forecasting performance and residual diagnostic tests suggest that FIGARCH generally outperforms RS-GARCH.     

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.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating yield spreads volatility using GARCH-type models

The primary focus of this study is on modeling the relationship between the volatility of corporate bond yield spreads and other covariates, including interest rate volatility, equity volatility, and rating. The purpose of this article is to apply various GARCH models to estimate the volatility of corporate bond yield spreads. This attempt is, to the best of our knowledge, the first to analyze the volatility of the yield spreads. In particular, this study utilizes standard GARCH and various asymmetric GARCH models, including E-GARCH, T-GARCH, P-GARCH, Q-GARCH, and I-GARCH models. We select the best fitting models for the noncallable (callable) case based on AIC, and it turns out Q-GARCH (T-GARCH) is the best fitting model. The estimation results indicate that our explanatory variables are statistically significant even at the 1% significance level when we apply the best fitting models. They are generally consistent, but we observe the presence of apparent differences. Our findings should be beneficial to practitioners, including investors.     

Volatility forecasting in European government bond markets

In this paper we examine the predictive power of the heterogeneous autoregressive (HAR) model for the return volatility of major European government bond markets. The results from HAR-type volatility forecasting models show that past short- and medium-term volatility are significant predictors of the term structure of the intraday volatility of European bonds with maturities ranging from 1 year up to 30 years. When we decompose bond market volatility into its continuous and discontinuous (jump) component, we find that the jump component is a significant predictor. Moreover, we show that feedback from past short-term volatility to forecasts of future volatility is stronger in the days that precede monetary policy announcements.     

Forecasting volatility with component conditional autoregressive range model

In this paper, we propose a component conditional autoregressive range (CCARR) model for forecasting volatility. The proposed CCARR model assumes that the price range comprises both a long-run (trend) component and a short-run (transitory) component, which has the capacity to capture the long memory property of volatility. The model is intuitive and convenient to implement by using the maximum likelihood estimation method. Empirical analysis using six stock market indices highlights the value of incorporating a second component into range (volatility) modelling and forecasting. In particular, we find that the proposed CCARR model fits the data better than the CARR model, and that it generates more accurate out-of-sample volatility forecasts and contains more information content about the true volatility than the popular GARCH, component GARCH and CARR models.     

Forecasting realized volatility of agricultural commodities

We forecast the realized and median realized volatility of agricultural commodities using variants of the heterogeneous autoregressive (HAR) model. We obtain tick-by-tick data on five widely-traded agricultural commodities (corn, rough rice, soybeans, sugar, and wheat) from the CME/ICE. Real out-of-sample forecasts are produced for between 1 and 66 days ahead. Our in-sample analysis shows that the variants of the HAR model which decompose volatility measures into their continuous path and jump components and incorporate leverage effects offer better fitting in the predictive regressions. However, we demonstrate convincingly that such HAR extensions do not offer any superior predictive ability in their out-of-sample results, since none of these extensions produce significantly better forecasts than the simple HAR model. Our results remain robust even when we evaluate them in a Value-at-Risk framework. Thus, there is no benefit from including more complexity, related to the volatility decomposition or relative transformations of the volatility, in the forecasting models.