Accurate Volatility Forecasts Research Articles

Functional volatility forecasting

AbstractWidely used volatility forecasting methods are usually based on low‐frequency time series models. Although some of them employ high‐frequency observations, these intraday data are often summarized into low‐frequency point statistics, for example, daily realized measures, before being incorporated into a forecasting model. This paper contributes to the volatility forecasting literature by instead predicting the next‐period intraday volatility curve via a functional time series forecasting approach. Asymptotic theory related to the estimation of latent volatility curves via functional principal analysis is formally established, laying a solid theoretical foundation of the proposed forecasting method. In contrast with nonfunctional methods, the proposed functional approach fully exploits the rich intraday information and hence leads to more accurate volatility forecasts. This is confirmed by extensive comparisons between the proposed method and those widely used nonfunctional methods in both Monte Carlo simulations and an empirical study on a number of stocks and equity indices from the Chinese market.

Forecasting the volatility of crude oil futures: A time‐dependent weighted least squares with regularization constraint

AbstractParameter instability and model uncertainty are two key problems affecting forecasting outcomes. In this paper, we propose a time‐dependent weighted least squares with ridge constraint (TWLS‐Ridge) to solve the above two problems in the forecasting procedure. The new TWLS‐Ridge approach is applied to the heterogenous autoregressive realized volatility model and its various extensions. The empirical results suggest that TWLS‐Ridge produces more accurate volatility forecasts than several alternative models dealing with parameter instability and model uncertainty. The superior performance of TWLS‐Ridge is robust under different forecast horizons, evaluation periods, and loss functions. An investor with mean–variance preference can improve utility using TWLS‐Ridge forecasts of oil volatility instead of ordinary least squares model forecasts.

Forecasting the volatility of European Union allowance futures with time-varying higher moments and time-varying risk aversion

There is increasing evidence that European Union allowance (EUA) futures return distributions exhibit features of time-varying higher moments (skewness and kurtosis), which plays an important role in modeling and forecasting EUA futures volatility. Moreover, a number of studies have shown that time-varying risk aversion (RA) contains useful information for forecasting EUA futures volatility. In light of this, this paper proposes the GARCH-MIDAS with skewness and kurtosis (hereafter GARCH-MIDAS-SK) to empirically investigate the impact and predictive role of RA on EUA futures volatility. Our empirical results show that RA has a significantly negative impact on the long-term volatility of EUA futures. The EUA futures return distributions exhibit obvious features of time-varying higher moments. Incorporating RA and time-varying higher moments improves the in-sample fitting of the model. Furthermore, out-of-sample results suggest that incorporating RA and time-varying higher moments leads to significantly more accurate volatility forecasts. This finding is robust to alternative out-of-sample forecasting windows.

Forecasting realized volatility: New evidence from time‐varying jumps in VIX

AbstractGiven that jumps in the implied volatility index (VIX) lead to rapid changes in the level of volatility, they may contain significant predictive information for the realized variance (RV) of stock returns. Against this backdrop, the present study proposes to extend the heterogeneous autoregressive (HAR) model using the information content of time‐varying jumps occurring in VIX. We find that jumps in VIX have positive impacts on the RV of S&P 500 index and that the proposed HAR‐RV approach generates more accurate volatility forecasts than do the existing HAR‐RV type models. Importantly, these results hold for short‐, medium‐, and long‐term volatility components.

A two-component realized exponential generalized autoregressive conditional heteroscedasticity model

This paper proposes a two-component realized exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model – an extension of the realized EGARCH model – for the joint modeling of asset returns and realized measures of volatility. The proposed model assumes that the volatility of asset returns consists of two components: a long-run component and a short-run component. The model’s unique ability to capture the long-memory property of volatility distinguishes it from the standard realized EGARCH model. The model is convenient to implement within the framework of maximum likelihood estimation. We apply the two-component realized EGARCH model and a restricted version of the model (the two-component realized EGARCH model with only short-run leverage) to four stock indexes: the Standard & Poor’s 500 index, the Hang Seng index, the Nikkei 225 index and the Deutscher Aktienindex. The empirical study suggests that the two-component realized EGARCH model and its restricted version outperform the realized GARCH model, the realized EGARCH model and the realized heterogeneous autoregressive GARCH model in terms of in-sample fit. Further, an out-of-sample predictive analysis demonstrates that the two-component realized EGARCH model and its restricted version yield more accurate volatility forecasts than the alternatives.

On improving GARCH volatility forecasts for Bitcoin via a meta-learning approach

Modelling the volatility of Bitcoin, the cryptocurrency with the largest market share, has recently attracted considerable attention from researchers, practitioners and investors in financial markets and portfolio management. For this purpose, a wide variety of GARCH-type models have been employed. However, there is no consensus in the literature on which specification arising from the volatility equation and the assumed error distribution is better in an out-of-sample performance. This study tries to fill this gap by comparing the forecasting performances of 110 GARCH-type models for Bitcoin volatility. Furthermore, it proposes a new combining method based on support vector machines (SVM). This method effectively selects the set of superior models to perform meta-learning. The results indicate that the best performing GARCH specification depends on the loss function chosen, and the proposed method leads to more accurate volatility forecasts than those of the best GARCH-type models and other combining methods investigated.

Testing for the Number of Regimes in Financial Time Series GARCH Volatility

This paper investigates the optimal number of regimes that can better describe the corresponding conditional variance to different stock market indices. We compared several GARCH specifications using the Deviance Information Criterion (DIC), provided by the Bayesian approach Markov chain Monte Carlo (MCMC), considering many stylized facts such as asymmetry (i.e., leverage effect), fat-tailed distributions, and volatility clustering. The results show clearly that the four selected models exhibit a leverage effect and have at least two regimes, whatever the GARCH specifications are. In addition, the optimal number of regimes in the conditional variance process may change from a series to another depending on their structure. A predictive test using the Value-at-Risk confirms that the selected processes provide accurate volatility forecasts.

A Generalized Heterogeneous Autoregressive Model using the Market Index

This paper shows that generalizing the heterogeneous autoregressive model (HAR) with realized (co)variances and semi-(co)variances from the index leads to more accurate volatility forecasts. To circumvent the effects of the market microstructure noise arising from using high sampling frequencies, we adopt noise-robust estimators for the realized (co)variances and develop novel noise-robust estimators for the semi-(co)variances. To explore the sampling frequency at which the forecasting gains are maximized, we adopt a mixed-sampling approach that iterates over several sampling frequencies of the stock and the index. Our analysis shows that gains are maximized at the combination of a low (high) frequency on the stock (index). We illustrate that the observed forecasting gains translates into economic gains such that a risk-averse investor is willing to pay up to 57 annual basis points by adopting a model specification that utilizes the index information.

Heterogeneous market hypothesis approach for modeling unbiased extreme value volatility estimator in presence of leverage effect: An individual stock level study with economic significance analysis

This paper explores the role of heterogeneity and leverage effect on the predictability of the AddRS volatility estimator (Kumar & Maheswaran, 2014a) using daily, weekly and monthly volatility components. Similar to the model setting of heterogeneous autoregressive (HAR) model (Corsi, 2009), we introduce the frameworks (HAR – AddRS and HAR – AddRS – L) to incorporate the impact of heterogeneity and leverage effect in modeling the AddRS volatility estimator. We find that the heterogeneity and leverage effect significantly impact the volatility prediction and when taken together produce a better in-sample fit. To evaluate the out-of-sample performance of our new volatility models, we compare the forecasting performance of our models with that of other traditional benchmark models forecasts using the error statistic approach and Hansen (2005) superior predictive ability (SPA) test. The results show that the HAR – AddRS and HAR – AddRS – L models provide more accurate volatility forecasts for the out-of-sample. We also undertake the economic significance analysis to highlight that a substantial economic gain is achieved when the volatility forecasts based on the HAR – AddRS – L model are used to implement various trading strategies, however, the same is not true when the volatility forecasts are based on the traditional returns-based conditional volatility models.

Out-of-sample prediction of the oil futures market volatility: A comparison of new and traditional combination approaches

This paper aims to use both the standard and iterated combination approaches to accurately predict the oil futures market volatility. We further make a comprehensive comparison of the out-of-sample forecasting performance between the two paired combination approaches. According to both the Diebold-Mariano test and model confidence set test, the iterated combination approach generates significantly more accurate volatility forecasts than the standard counterpart. The Direction-of-Change test suggests that the iterated combination approach also has substantially higher directional accuracy. We document that these results are robust to various settings. Furthermore, a mean-variance investor can obtain sizeable economic gains when she uses the iterated combination forecasts instead of the standard ones to allocate her portfolio.

Forecasting stock market volatility: The role of technical variables

Accurate volatility forecasts are required by both market participants and policy makers. In this paper, we forecast stock return volatility by using a wide range of technical indicators constructed based on the past behavior of stock price, volatility and trading volume. Our out-of-sample results indicate that the incorporation of technical variables in the autoregression benchmark can produce significantly more accurate volatility forecasts. The forecasting performance of the combination of technical indicators is further compared with that of the popular economic indicators. Technical variables perform better than economic variables when the economy is an expansion, while the economic variables generate more accurate forecasts when the economy belongs a recession. These two types of variables provide complementary information over the business cycle. We obtain more reliable forecasts by combining all economic and technical information together than by combining either type of information alone.

Improving Volatility Forecasts Using Market‐Elicited Ambiguity Aversion Information

AbstractDistinguishing between risk and uncertainty, this paper proposes a volatility forecasting framework that incorporates asymmetric ambiguity shocks in the (exponential) generalized autoregressive conditional heteroskedasticity‐in‐mean conditional volatility process. Spanning 25 years of daily data and considering the differential role of investors' ambiguity attitudes in the gain and loss domains, our models capture a rich set of information and provide more accurate volatility forecasts both in‐sample and out‐of‐sample when compared to ambiguity‐free or risk‐based counterparts. Ambiguity‐based volatility‐timing trading strategies confirm the economic significance of our proposed framework and indicate that an annualized excess return of 3.2% over the benchmark could be earned from 1995 to 2014.

Asymmetric volatility in equity markets around the world

The observation that price declines usually lead to volatility increases is known as the asymmetric volatility effect and has become a stylized fact about the financial markets. We study asymmetric volatility effect in 19 equity indices from North America, Latin America, Europe, Asia and Australia, utilizing not only daily data and four GARCH class models, but also realized volatility calculated from high-frequency data within HAR class models. We first confirm the stylized fact that stock market indices around the world exhibit the asymmetric volatility effect. This effect is stronger for US and European market indices. Second, we find that the asymmetric volatility effect is strong enough to significantly improve out-of-sample forecasts of an accurate HAR volatility model. Third, we show that forecast improvements of the asymmetric volatility models are largest during periods of higher market volatility, when accurate volatility forecasts matter the most.

Asymmetric Volatility in Equity Markets Around the World

The observation that price declines usually lead to volatility increases is known as the asymmetric volatility effect and has become a stylized fact about the financial markets. We study asymmetric volatility effect in 19 equity indices from North America, Latin America, Europe, Asia and Australia, utilizing not only daily data and four GARCH class models, but also realized volatility calculated from high-frequency data within HAR class models. We first confirm the stylized fact that stock market indices around the world exhibit the asymmetric volatility effect. This effect is stronger for US and European market indices. Second, we find that the asymmetric volatility effect is strong enough to significantly improve out-of-sample forecasts of an accurate HAR volatility model. Third, we show that forecast improvements of the asymmetric volatility models are largest during periods of higher market volatility, when accurate volatility forecasts matter the most.

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.

Long memory volatility in Asian stock markets

PurposeThe purpose of this paper is to assess to what extent intraday data can explain and predict long-term memory.Design/methodology/approachThis article analysed the presence of long-memory volatility in five Asian equity indices, namely, SENSEX, CNIA, NIKKEI225, KO11 and FTSTI, using five-min intraday return series from 05 January 2015 to 06 August 2015 using two approaches, i.e. conditional volatility and realized volatility, for forecasting long-term memory. It employs conditional-generalized autoregressive conditional heteroscedasticity (GARCH), i.e. autoregressive fractionally integrated moving average (ARFIMA)-FIGARCH model and ARFIMA-asymmetric power autoregressive conditional heteroscedasticity (APARCH) models, and unconditional volatility realized volatility using autoregressive integrated moving average (ARIMA) and ARFIMA in-sample forecasting models to estimate the persistence of the long-term memory.FindingsGiven the GARCH framework, the ARFIMA-APARCH long-memory model gave the better forecast results signifying the importance of accounting for asymmetric information when modelling volatility in a financial market. Using the unconditional realized volatility results from the Singapore and Indian markets, the ARIMA model outperforms the ARFIMA model in terms of forecast performance and provides reasonable forecasts.Practical implicationsThe issue of long memory has important implications for the theory and practice of finance. It is well-known that accurate volatility forecasts are important in a variety of settings including option and other derivatives pricing, portfolio and risk management.Social implicationsIt could be said that using long-memory augmented models would give better results to investors so that they could analyse the market trends in returns and volatility in a more accurate manner and reach at an informed decision. This is useful to minimize the risks.Originality/valueThis research enhances the literature by estimating the influence of intraday variables on daily volatility. This is one of very few studies that uses conditional GARCH framework models and unconditional realized volatility estimates for forecasting long-term memory. The authors find that the methods complement each other.

Volatility Forecasting with the Multifractal Model of Asset Returns

This paper presents an empirical application of the Multifractal Model of Asset Returns (MMAR) to intraday stock prices, with a goal of generating accurate volatility forecasts. Intraday stock volatility exhibits long tails, persistence, and strong evidence of moment scaling. This allows us to apply the MMAR. A forecasting method for the MMAR is implemented through Monte Carlo simulation, and this forecasting method is compared to Generalized Autoregressive Conditional Heteroskedasticity (GARCH) alternatives over several testing samples. The MMAR significantly outperformed the GARCH models. This suggests that the framework of multifractality has a large potential for further development and application within finance.

Heterogeneous autoregressive model with structural break using nearest neighbor truncation volatility estimators for DAX.

High frequency financial data modelling has become one of the important research areas in the field of financial econometrics. However, the possible structural break in volatile financial time series often trigger inconsistency issue in volatility estimation. In this study, we propose a structural break heavy-tailed heterogeneous autoregressive (HAR) volatility econometric model with the enhancement of jump-robust estimators. The breakpoints in the volatility are captured by dummy variables after the detection by Bai–Perron sequential multi breakpoints procedure. In order to further deal with possible abrupt jump in the volatility, the jump-robust volatility estimators are composed by using the nearest neighbor truncation approach, namely the minimum and median realized volatility. Under the structural break improvements in both the models and volatility estimators, the empirical findings show that the modified HAR model provides the best performing in-sample and out-of-sample forecast evaluations as compared with the standard HAR models. Accurate volatility forecasts have direct influential to the application of risk management and investment portfolio analysis.

Forecasting volatility with interacting multiple models

We examine the performance of Kalman filter techniques in forecasting volatility. We find that the simple implementation of an online Kalman filtering procedure that combines commonly used forecasting models with market-based estimates improves the accuracy of volatility forecasts. Furthermore, we demonstrate that the Interacting Multiple Model algorithm, which combines multiple Kalman filters, provides the most accurate volatility forecasts overall.

Oil prices changes and volatility in sector stock returns: Evidence from Australia, New Zealand, China, Germany and Norway

The paper examines the exposure of sectoral stock returns to oil price changes in Australia, China, Germany, New Zealand and Norway over the period 2000-2015 using weekly data drawn from DataStream. The issue of volatility has important implications for the theory of finance and as is well-known accurate volatility forecasts are important in a variety of settings including option and other derivatives pricing, portfolio and risk management (e.g. in the calculation of hedge ratios and Value-at-Risk measures), and trading strategies (David and Ruiz, 2009). This study adopts GARCH and EGARCH to understand the relationship between the returns and volatility. The findings using GARCH (EGARCH) models suggests that in the case of Germany eight (nine) out of ten sectors returns can be explained by the volatility of past oil price in Germany, while in the case of Australia, six (seven) out of ten sector returns are sensitive to the oil price changes with the exception of Industrials, Consumer Goods, Health care and Utilities. While in China and New Zealand five sectors are found sensitive to oil price changes and three sectors in Norway, namely Oil & Gas, Consumer Services and Financials. Secondly, this paper also investigated the exposure of the stock returns to oil price changes using market index data as a proxy using GARCH or EGARCH model. The results indicated that the stock returns are sensitive to the oil price changes and have leverage effects for all the five countries. Further, the findings also suggests that sector with more constituents is likely to have leverage effects and vice versa. The results have implications to market participants to make informed decisions about a better portfolio diversification for minimizing risk and adding value to the stocks.