Realized Volatility Forecasting Research Articles

Does VPIN provide predictive information for realized volatility forecasting: evidence from Chinese stock index futures market

PurposeUsing intraday data, the authors explore the forecast ability of one high frequency order flow imbalance measure (OI) based on the volume-synchronized probability of informed trading metric (VPIN) for predicting the realized volatility of the index futures on the China Securities Index 300 (CSI 300).Design/methodology/approachThe authors employ the heterogeneous autoregressive model for realized volatility (HAR-RV) and compare the forecast ability of models with and without the predictive variable, OI.FindingsThe empirical results demonstrate that the augmented HAR model incorporating OI (HARX-RV) can generate more precise forecasts, which implies that the order imbalance measure contains substantial information for describing the volatility dynamics.Originality/valueThe study sheds light on the relation between high frequency trading behavior and volatility forecasting in China's index futures market and reveals the underlying market mechanisms of liquidity-induced volatility.

Sparse vector heterogeneous autoregressive modeling for realized volatility

We propose a sparse vector heterogeneous autoregressive (VHAR) model for realized volatility forecasting. As a multivariate extension of a heterogeneous autoregressive model, a VHAR model can consider the dynamics of multinational stock volatilities in a compact manner. A sparse VHAR is estimated using adaptive lasso and some theoretical properties are provided. In practice, our sparse VHAR model can improve forecasting performance and explicitly show the connectivity between stock markets. In particular, our empirical analysis shows that the NASDAQ market had the strongest influence on stock market volatility worldwide in the 2010s.

Realized volatility forecasting and volatility spillovers: Evidence from Chinese non‐ferrous metals futures

AbstractWe study the prediction of realized volatility of non‐ferrous metals futures traded on the Shanghai Futures Exchange from March 2011 to December 2017. A dynamic model averaging model is employed to combine multiple prediction models using time‐varying weights based on individual model performance. Empirical results also reveal that models incorporating volatility spillovers across metals are important for forecast combinations, and short‐term spillovers have a stronger impact than long‐term spillovers. This approach offers the best forecasting performance and allows users to identify the most dominant model at any given time and demonstrate when and how volatility transmission from another metal is valuable for forecasting. We also find evidence of distinct trading behaviours in emerging and developed markets.

Increasing the Information Dynamics of Realized Volatility Forecasts

This paper draws upon several distinct contributions to improve the out-of- sample forecasting performance of realized volatility models. More specifically, we retain the rolling-sample idea of Andreou and Ghysels (2002) to propose a new approach we call the Rolling Realized Volatility (RRV ), which samples consecutive high-frequency squared returns regardless of whether they originate from the same trading session like in the traditional approach. This new approach yields a sample approximately M times larger than the traditional approach, where M is the intraday sampling frequency. The new approach has at least two advantages. First, having more observations increases the informational dynamics of the OLS regression. Second, the Rolling method accounts for the serial correlation between the last returns in day t − 1 and the first returns in day t. We test competing out-of-sample forecast losses from the new approach against those of the traditional method for the S&P 500 and 26 Dow Jones Industrial Average stocks. Using several state-of-the-art realized volatility models, both a simulation and an empirical exercise strongly suggest the Rolling approach yields superior out-of-sample performance over the traditional approach.

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.

Realized volatility forecasting: Robustness to measurement errors

In this paper, we suggest how to handle the issue of the heteroskedasticity of measurement errors when specifying dynamic models for the conditional expectation of realized variance. We show that either adding a GARCH correction within an asymmetric extension of the HARclass (AHAR-GARCH), or working within the class of asymmetric multiplicative error models (AMEM) greatly reduces the need for quarticity/quadratic terms to capture attenuation bias. This feature in AMEM can be strengthened by considering regime specific dynamics. Model Confidence Sets confirm this robustness both in- and out-of-sample for a panel of 28 big caps and the S&P500 index.

Multivariate realized volatility forecasts of agricultural commodity futures

AbstractWe forecast the multivariate realized volatility of agricultural commodity futures by constructing multivariate heterogeneous autoregressive (MHAR) models with flexible heteroscedastic error structures that allow for non‐Gaussian distribution, stochastic volatility, and heteroscedastic and serial dependence. We evaluate the forecast performances of various models based on both statistical and economic criteria. The in‐sample and out‐of‐sample results suggest that the proposed MHAR models allowing for flexible heteroscedastic covariance structures outperform the benchmark MHAR models. In addition, the proposed Bayesian MHAR models allowing for t innovations improve both in‐sample and out‐of‐sample forecast performance of the corresponding MHAR models with Gaussian innovations.

Futures-based forecasts: How useful are they for oil price volatility forecasting?

Oil price volatility forecasts have recently attracted the attention of many studies in the energy finance field. The literature mainly concentrates its attention on the use of daily data, using GARCH-type models. It is only recently that efforts to use more informative intra-day data to forecast oil price realized volatility have been made. Despite all these previous efforts, no study has examined the usefulness of futures-based models for oil price realized volatility forecasting, although the use of such models is extensive for oil price predictions. This study fills this void and shows that futures-based forecasts based on intra-day data provide informative forecasts for horizons that span between 1-day and 66-days ahead. More importantly, these results hold true even during turbulent times for the oil market, such as the Global Financial Crisis of 2007–09 and the oil collapse period of 2014–15.

Improving volatility forecasting based on Chinese volatility index information: Evidence from CSI 300 index and futures markets

This paper investigates whether iVX, the newly launched implied volatility index in China contains incremental information about volatility forecasting. We use high frequency data of Chinese CSI 300 stock index and futures to calculate realized volatility, then estimate various constant coefficients and time-varying coefficients HAR models (TVC-HAR), and finally adopt one-step and smooth multi-step rolling forecasting methods to evaluate the forecasting errors. Our analysis confirms that iVX does have significant influence to the realized volatility forecasting. Both the in-sample and out-of-sample forecasting errors indicate that iVX plays a crucial role to volatility forecasting, combining both continuous volatility, jump volatility and iVX information leads to best performance. TVC-HAR models outperform HAR models for multi-step ahead forecasting while with iVX as regressor perform best for one-step ahead forecasting. TVC-HAR models with iVX as driven factor is more suitable for index while models with time as the driven factor perform better for futures. MCS test further confirms the superiority of the selected models in volatility forecasting. Our study is important for financial market risk management and the healthy development of derivatives market in China.

Forecasting Market Index Volatility Using Ross-Recovered Distributions

Ross (2015) shows that options data can reveal the market’s true expectations. Adapting this approach to index options (S&P, FTSE, CAC, SMI and DAX), we separate option-implied volatility into Ross-recovered true expected volatility and a risk preference factor. We investigate whether these factors perform better to forecast realized volatility if constructed locally or globally, yielding new insights to understand international dynamics in risk expectations and preferences. We find evidence of significantly improved realized volatility forecasts. Models using Ross-recovered value-weighted global measures of risk preferences have the best forecasting performances across indices. Risk preferences are best measured globally. Overall, the findings suggest that the Recovery Theorem is useful empirically and accurately recovers the true expected returns distribution and its associated pricing kernel.

Multiple days ahead realized volatility forecasting: Single, combined and average forecasts

The task of this paper is the enhancement of realized volatility forecasts. We investigate whether a mixture of predictions (either the combination or the averaging of forecasts) can provide more accurate volatility forecasts than the forecasts of a single model. We estimate long-memory and heterogeneous autoregressive models under symmetric and asymmetric distributions for the major European Union stock market indices and the exchange rates of the Euro.The majority of models provide qualitatively similar predictions for the next trading day's volatility forecast. However, with regard to the one-week forecasting horizon, the heterogeneous autoregressive model is statistically superior to the long-memory framework. Moreover, for the two-weeks-ahead forecasting horizon, the combination of realized volatility predictions increases the forecasting accuracy and forecast averaging provides superior predictions to those supplied by a single model. Finally, the modeling of volatility asymmetry is important for the two-weeks-ahead volatility forecasts.

Dynamics of financial returns densities: A functional approach applied to the Bovespa intraday index

We model the stochastic evolution of the probability density functions (PDFs) of Ibovespa intraday returns over business days, in a functional time series framework. We find evidence that the dynamic structure of the PDFs reduces to a vector process lying in a two-dimensional space. Our main contributions are as follows. First, we provide further insights into the finite-dimensional decomposition of the curve process: it is shown that its evolution can be interpreted as a dynamic dispersion-symmetry shift. Second, we provide an application to realized volatility forecasting, with a forecasting ability that is comparable to those of HAR realized volatility models in the model confidence set framework.

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.

Copula–Based vMEM Specifications versus Alternatives: The Case of Trading Activity

We discuss several multivariate extensions of the Multiplicative Error Model to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional expectations of the variables can be simultaneously estimated. Results with realized volatility, volumes and number of trades of the JNJ stock show that significantly superior realized volatility forecasts are delivered with a fully interdependent vMEM relative to a single equation. Alternatives involving log–Normal or semiparametric formulations produce substantially equivalent results.

Realized volatility forecast of agricultural futures using the HAR models with bagging and combination approaches

In order to reduce the uncertainty associated with a single predictor model, we incorporate the bagging and combination approaches into a HAR model with the lags of realized volatility and other potential predictors to forecast the realized volatility of agricultural commodity futures in China. We evaluate the performances of the two approaches by employing the mean square forecast error (MSFE) loss function, the modified DM test and the model confidence set (MCS) test at the multiple horizons over the three out-of-sample periods. We find that the realized forecasts from the HAR model with bagging and principal component (PC) combination approaches produce the lowest MSFE at relatively longer forecast horizons. We also find that the simple average of the forecasts from the HAR models with bagging and PC combination methods leads to a further reduction in MSFE, suggesting that they are the effective methods to forecast the realized volatility of agricultural commodity futures in China.

Realized volatility forecasting of agricultural commodity futures using the HAR model with time-varying sparsity

We develop a time-varying HAR model where both the predictors and the regression coefficients are allowed to change over time, and use it to forecast the realized volatility in the fast-growing agricultural commodity futures markets of China. The proposed model is constructed by incorporating all potential predictors in a time-varying HAR framework, and giving the independent normal-gamma autoregressive (NGAR) process priors to the regression coefficients. The out-of-sample forecast results show that the proposed HAR model with time-varying sparsity improves the forecast performances substantially relative to both the simple HAR model and more sophisticated HAR-type models in almost all cases. Finally, the forecast performance of the proposed model is robust to the alternative proxies of volatility.

Realized Volatility Forecasting of Agricultural Commodity Futures Using Long Memory and Regime Switching

AbstractWe investigate the dynamic properties of the realized volatility of five agricultural commodity futures by employing the high‐frequency data from Chinese markets and find that the realized volatility exhibits both long memory and regime switching. To capture these properties simultaneously, we utilize a Markov switching autoregressive fractionally integrated moving average (MS‐ARFIMA) model to forecast the realized volatility by combining the long memory process with regime switching component, and compare its forecast performances with the competing models at various horizons. The full‐sample estimation results show that the dynamics of the realized volatility of agricultural commodity futures are characterized by two levels of long memory: one associated with the low‐volatility regime and the other with the high‐volatility regime, and the probability to stay in the low‐volatility regime is higher than that in the high‐volatility regime. The out‐of‐sample volatility forecast results show that the combination of long memory with switching regimes improves the performance of realized volatility forecast, and the proposed model represents a superior out‐of‐sample realized volatility forecast to the competing models. Copyright © 2016 John Wiley & Sons, Ltd.

Global equity market volatility spillovers: A broader role for the United States

Rapach et al. (2013) recently showed that U.S. equity market returns contain valuable information for improving return forecasts in global equity markets. In this study, we extend the work of Rapach et al. (2013) and examine whether U.S.-based equity market information can be used to improve realized volatility forecasts in a large cross-section of international equity markets. We use volatility data for the U.S. and 17 foreign equity markets from the Oxford Man Institute’s realized library, and augment our benchmark HAR model with U.S. equity market volatility information for each foreign equity market. We show that U.S. equity market volatility information improves the out-of-sample forecasts of realized volatility substantially in all 17 foreign equity markets that we consider. Not only are these forecast gains highly significant, they also produce out-of-sample R2 values of between 4.56% and 14.48%, with 9 being greater than 10%. The improvements in out-of-sample forecasts remain statistically significant for horizons up to one month ahead. A substantial part of these predictive gains is driven by forward-looking volatility, as captured by the VIX.

Copula-Based Specification of Vector MEMs

The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of sufficiently flexible probability density functions for such processes by suggesting a copula function approach to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate this vector MEM with an application to the interactions between realized volatility, volume and the number of trades. We show that significantly superior realized volatility forecasts are delivered in the presence of other trading activity indicators and contemporaneous correlations.

Global Equity Market Volatility Spillovers: A Broader Role for the United States

Rapach et al. (2013) have recently shown that U.S. equity market returns carry valuable information to improve return forecasts in global equity markets. In this study, we extend the work of Rapach et al. (2013) and examine if U.S. based equity market information can be used to improve realized volatility forecasts in a large cross-section of international equity markets. We use volatility data for the U.S. and 17 foreign equity markets from the Oxford Man Institute’s realized library and augment for each foreign equity market our benchmark HAR model with U.S. equity market volatility information. We show that U.S. equity market volatility information substantially improves out-of-sample forecasts of realized volatility in all 17 foreign equity markets that we consider. Forecast gains are not only highly significant, but produce out-of-sample R 2 values between 4.56% and 14.48%, with 12 of these being greater than 10%. The improvements in out-of-sample forecasts remain statistically significant for horizons up to 1 month ahead. A substantial part of the predictive gains are driven by forward looking volatility as captured by the VIX.