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 the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

A dynamic Nelson-Siegel yield curve model with Markov switching

This paper proposes a model to better capture persistent regime changes in the interest rates of the US term structure. While the previous literature on this matter proposes that regime changes in the term structure are due to persistent changes in the conditional mean and volatility of interest rates we find that changes in a single parameter that determines the factor loadings of the model better captures regime changes. We show that this model gives superior in-sample forecasting performance as compared to a baseline model and a volatility-switching model. In general, we find compelling evidence that the extracted factors from our term structure models are closely related with various economic variables. Furthermore, we investigate and find evidence that the effects of macroeconomic phenomena such as monetary policy, inflation expectations, and real economic activity differ according to the particular regime realized for the term structure. In particular, we identify the periods where monetary policy appears to have a greater effect on the yield curve, and the periods where inflation expectations seem to have a greater effect in yield determination. We also find convincing evidence of a relationship between the regimes estimated by the various switching models with economic activity and monetary policy.     

Conditional Markov regime switching model applied to economic modelling

In this paper we discuss the calibration issues of regime switching models built on mean-reverting and local volatility processes combined with two Markov regime switching processes. In fact, the volatility structure of these models depends on a first exogenous Markov chain whereas the drift structure depends on a conditional Markov chain with respect to the first one. The structure is also assumed to be Markovian and both structure and regime are unobserved. Regarding this construction, we extend the classical Expectation–Maximization (EM) algorithm to be applied to our regime switching model. We apply it to economic data (Euro/Dollar (USD) foreign exchange rate and Brent oil price) to show that such modelling clearly identifies both mean reverting and volatility regime switches. Moreover, it allows us to make economic interpretations of this regime classification as in some financial crises or some economic policies.     

Crude oil price volatility dynamics and the great recession

Using a very simple econometric framework, we identify two major changes in the dynamics of crude oil price volatility based on data from 1997 to 2017. More precisely, we model weekly West Texas Intermediate (WTI) crude oil price realized volatility in a two-regime setting, one where realized volatility evolves as a plain autoregressive (AR) process (static), and the other where the level, persistence and innovation volatility of the AR process are subject to changes (dynamic). We use a Markov chain to model the probability that the process is in the static regime. The post Great Recession period sees a longer duration of the dynamic regime as well as smaller changes in the level and conditional volatility of realized volatility when switching actually occurs. Crude oil volatility also responds more aggressively to changes in economic variables, such as the t-bill rate and equity market volatility in the dynamic regime.     

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.     

S&P 500 volatility,volatility regimes,and economic uncertainty

We assess the relationship between regime-dependent volatility in S&P 500, economic policy uncertainty, the S&P 500 bull and bear sentiment spread (bb_sp), as well as the Chicago Board Options Exchange's VIX over the period 2000–2018. Our findings from two-covariate GARCH–MIDAS (GM) methodology, regime switching Markov Chain, and quantile regressions suggest that the association of realized volatility and sentiment varies across high- and low-volatility regimes and depends on investors’ sensitivity toward incidents of market uncertainties under these regimes. The findings suggest that these indicators may not be useful in volatility forecasting, especially under high-volatility regimes.     

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.     

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.     

What should the value of lambda be in the exponentially weighted moving average volatility model?

Forecasting volatility is fundamental to forecasting parametric models of value-at-risk. The exponentially weighted moving average (EWMA) volatility model is the recommended model for forecasting volatility by the Riskmetrics group. For monthly data, the lambda parameter of the EWMA model is recommended to be set to 0.97. In this study, we empirically investigate if this is the optimal value of lambda in terms of forecasting volatility. Employing monthly realized volatility as the benchmark for testing the value of lambda, it is found that a value of lambda of 0.97 is far from optimal. The tests are robust to a variety of test statistics. It is further found that the optimal value of lambda is time varying and should be based upon recent historical data. The article offers a practical method to increase the reliability and accuracy of value-at-risk forecasts that can be easily implemented within an Excel spreadsheet.     

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.     

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.     

Testing volatility persistence on Markov switching stochastic volatility models

In the literature, some researchers found that the high persistence of the volatility can be caused by Markov regime switching. This concern can be reflected as a unit root problem on the basis of Markov switching models. In this paper, our main purpose is to provide a Bayesian unit root testing approach for Markov switching stochastic volatility (MSSV) models. We illustrate the developed approach using S&P 500 daily return covering the subprime crisis started in 2008.     

ANALYTICAL EVALUATION OF VOLATILITY FORECASTS*

Estimation and forecasting for realistic continuous‐time stochastic volatility models is hampered by the lack of closed‐form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys (Econometrica, 71 (2003), 579–625) advocate forecasting integrated volatility via reduced‐form models for the realized volatility, constructed by summing high‐frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced‐form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.     

Modelling conditional moments and correlation with the continuous hidden-threshold-skew-normal distribution

A key issue in modelling conditional densities of returns of financial assets is the time-variation of conditional volatility. The classic econometric approach models volatility of returns with the generalized autoregressive conditional heteroscedasticity (GARCH) models where the conditional mean and the conditional volatility depend only on historical prices. We propose a new family of distributions in which the conditional distribution depends on a latent continuous factor with a continuum of states. The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. The distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. We show empirically that this distribution outperforms its main competitor, the mixed normal conditional distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.     

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.     

Improving GARCH volatility forecasts with regime-switching GARCH

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-period-ahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better out-of-sample volatility forecasts. First Version Received: November 2000/Final Version Received: August 2001     

Realized volatility models and alternative Value-at-Risk prediction strategies

We assess the Value-at-Risk (VaR) forecasting performance of recently proposed realized volatility (RV) models combined with alternative parametric and semi-parametric quantile estimation methods. A benchmark inter-daily GJR-GARCH model is also employed. Based on four asset classes, i.e. equity, FOREX, fixed income and commodity, and a turbulent six year out-of-sample period (2007–2013), we find that statistical accuracy and regulatory compliance is essentially improved when we use quantile methods which account for the fat tails and the asymmetry of the innovations distribution. In particular, empirical analysis gives evidence in favor of the skewed student distribution and the Extreme Value Theory (EVT) method. Nonetheless, efficiency of VaR estimates, as defined by the minimization of Basel II capital requirements and its opportunity costs, is reassured only with the use of realized volatility models. Overall, empirical evidence support the use of an asymmetric HAR realized volatility model coupled with the EVT method since it produces statistically accurate VaR forecasts which comply with Basel II accuracy mandates and allows for more efficient capital allocations.     

The impact of trading volume,number of trades and overnight returns on forecasting the daily realized range

Intraday data of 26 German stocks are used to investigate whether the information contained in trading volume and number of trades as well as in various specifications of overnight returns can improve one-step-ahead volatility forecasts. For this purpose, a HAR model of the realized range adjusted for discrete trading is augmented by each of these variables and compared with the model's default form. The results show that the considered liquidity measures lead to very modest improvements in forecasting performance. The overnight returns exhibit some in-sample forecasting power. However, the accuracy improvement of out-of-sample forecasts is unequivocally non-significant.     

Output volatility in Australia

A number of papers have documented a significant decline in real GDP volatility in several major OECD economies. Some authors have presented evidence to suggest that this is the outcome of a one-off structural break from a high to low volatility state whilst others have estimated regime switching models that indicate low volatility regime states have dominated in recent years. This article provides further evidence on the general properties of output volatility for Australia, including evidence of a significant moderation in output volatility for the country that occurred in the early 1980s. Estimates of various GARCH models of real GDP growth are also provided to further examine shorter term volatility features of the Australian economy that are associated with its business-cycle. A regime shift dummy is maintained in all models of the conditional variance in order to account for the regime shift in volatility and evidence is found of significant business-cycle effects, including leverage effects and asymmetries that suggest recessions are times of higher output volatility than economic expansions. Overall, it is concluded that the so-called ‘Great Moderation’ in macroeconomic instability, as documented here for Australia, is a result of a myriad of economic, institutional and policymaking changes.