Forecasting stock market volatility using (non-linear) Garch models

In this paper we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng, 1993) and the Glosten, Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations such as the 1987 stock market crash and that the GJR model cannot be recommended for forecasting.     

The role of jumps in the agricultural futures market on forecasting stock market volatility: New evidence

In this study, we explore the effect of cojumps within the agricultural futures market, and cojumps between the agricultural futures market and the stock market, on stock volatility forecasting. Also, we take into account large and small components of cojumps. We have several noteworthy findings. First, large jumps may lead to more substantial fluctuations and are more powerful than small jumps. The effect of cojumps and their decompositions on future volatility are mixed. Second, a model including large and small cojumps between the agricultural futures market and the stock market can achieve a higher forecasting accuracy, implying that large and small cojumps contain more useful predictive information than cojumps themselves. Third, our conclusions are robust based on various robustness tests such as the realized kernel, expanding forecasts, different forecasting windows, different jump tests, and different threshold values.     

Forecasting volatility

In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model‐based volatility, and show that these volatility processes exhibit an extremely slow mean‐reverting behavior and possible long memory. For this reason, we explicitly model the near‐unit root behavior of volatility and construct median unbiased forecasts by approximating the finite‐sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next‐period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Forecasting realized volatility of oil futures market: A new insight

In this study we propose several new variables, such as continuous realized semi‐variance and signed jump variations including jump tests, and construct a new heterogeneous autoregressive model for realized volatility models to investigate the impacts that those new variables have on forecasting oil price volatility. In‐sample results indicate that past negative returns have greater effects on future volatility than that of positive returns, and our new signed jump variations have a significantly negative influence on the future volatility. Out‐of‐sample empirical results with several robust checks demonstrate that our proposed models can not only obtain better performance in forecasting volatility but also garner larger economic values than can the existing models discussed in this paper.     

Forecasting and trading currency volatility: an application of recurrent neural regression and model combination

In this paper, we examine the use of non‐parametric Neural Network Regression (NNR) and Recurrent Neural Network (RNN) regression models for forecasting and trading currency volatility, with an application to the GBP/USD and USD/JPY exchange rates. Both the results of the NNR and RNN models are benchmarked against the simpler GARCH alternative and implied volatility. Two simple model combinations are also analysed. The intuitively appealing idea of developing a nonlinear nonparametric approach to forecast FX volatility, identify mispriced options and subsequently develop a trading strategy based upon this process is implemented for the first time on a comprehensive basis. Using daily data from December 1993 through April 1999, we develop alternative FX volatility forecasting models. These models are then tested out‐of‐sample over the period April 1999–May 2000, not only in terms of forecasting accuracy, but also in terms of trading efficiency: in order to do so, we apply a realistic volatility trading strategy using FX option straddles once mispriced options have been identified. Allowing for transaction costs, most trading strategies retained produce positive returns. RNN models appear as the best single modelling approach yet, somewhat surprisingly, model combination which has the best overall performance in terms of forecasting accuracy, fails to improve the RNN‐based volatility trading results. Another conclusion from our results is that, for the period and currencies considered, the currency option market was inefficient and/or the pricing formulae applied by market participants were inadequate. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluating volatility and interval forecasts

A widely used approach to evaluating volatility forecasts uses a regression framework which measures the bias and variance of the forecast. We show that the associated test for bias is inappropriate before introducing a more suitable procedure which is based on the test for bias in a conditional mean forecast. Although volatility has been the most common measure of the variability in a financial time series, in many situations confidence interval forecasts are required. We consider the evaluation of interval forecasts and present a regression‐based procedure which uses quantile regression to assess quantile estimator bias and variance. We use exchange rate data to illustrate the proposal by evaluating seven quantile estimators, one of which is a new non‐parametric autoregressive conditional heteroscedasticity quantile estimator. The empirical analysis shows that the new evaluation procedure provides useful insight into the quality of quantile estimators. Copyright © 1999 John Wiley & Sons, Ltd.     

Modeling and forecasting aggregate stock market volatility in unstable environments using mixture innovation regressions

We perform Bayesian model averaging across different regressions selected from a set of predictors that includes lags of realized volatility, financial and macroeconomic variables. In our model average, we entertain different channels of instability by either incorporating breaks in the regression coefficients of each individual model within our model average, breaks in the conditional error variance, or both. Changes in these parameters are driven by mixture distributions for state innovations (MIA) of linear Gaussian state‐space models. This framework allows us to compare models that assume small and frequent as well as models that assume large but rare changes in the conditional mean and variance parameters. Results using S&P 500 monthly and quarterly realized volatility data from 1960 to 2014 suggest that Bayesian model averaging in combination with breaks in the regression coefficients and the error variance through MIA dynamics generates statistically significantly more accurate forecasts than the benchmark autoregressive model. However, compared to a MIA autoregression with breaks in the regression coefficients and the error variance, we fail to provide any drastic improvements.     

Forecasting stock volatility in the presence of extreme shocks: Short-term and long-term effects

This paper introduces a novel generalized autoregressive conditional heteroskedasticity–mixed data sampling–extreme shocks (GARCH-MIDAS-ES) model for stock volatility to examine whether the importance of extreme shocks changes in different time ranges. Based on different combinations of the short- and long-term effects caused by extreme events, we extend the standard GARCH-MIDAS model to characterize the different responses of the stock market for short- and long-term horizons, separately or in combination. The unique timespan of nearly 100 years of the Dow Jones Industrial Average (DJIA) daily returns allows us to understand the stock market volatility under extreme shocks from a historical perspective. The in-sample empirical results clearly show that the DJIA stock volatility is best fitted to the GARCH-MIDAS-SLES model by including the short- and long-term impacts of extreme shocks for all forecasting horizons. The out-of-sample results and robustness tests emphasize the significance of decomposing the effect of extreme shocks into short- and long-term effects to improve the accuracy of the DJIA volatility forecasts.     

Volatility Forecasting via MIDAS,HAR and their Combination: An Empirical Comparative Study for IBOVESPA

In this paper we compare several multi‐period volatility forecasting models, specifically from MIDAS and HAR families. We perform our comparisons in terms of out‐of‐sample volatility forecasting accuracy. We also consider combinations of the models' forecasts. Using intra‐daily returns of the BOVESPA index, we calculate volatility measures such as realized variance, realized power variation and realized bipower variation to be used as regressors in both models. Further, we use a nonparametric procedure for separately measuring the continuous sample path variation and the discontinuous jump part of the quadratic variation process. Thus MIDAS and HAR specifications with the continuous sample path and jump variability measures as separate regressors are estimated. Our results in terms of mean squared error suggest that regressors involving volatility measures which are robust to jumps (i.e. realized bipower variation and realized power variation) are better at forecasting future volatility. However, we find that, in general, the forecasts based on these regressors are not statistically different from those based on realized variance (the benchmark regressor). Moreover, we find that, in general, the relative forecasting performances of the three approaches (i.e. MIDAS, HAR and forecast combinations) are statistically equivalent. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting volatility of emerging stock markets: linear versus non‐linear GARCH models

ARCH and GARCH models are substantially used for modelling volatility of time series data. It is proven by many studies that if variables are significantly skewed, linear versions of these models are not sufficient for both explaining the past volatility and forecasting the future volatility. In this paper, we compare the linear(GARCH(1,1)) and non‐linear(EGARCH) versions of GARCH model by using the monthly stock market returns of seven emerging countries from February 1988 to December 1996. We find that for emerging stock markets GARCH(1,1) model performs better than EGARCH model, even if stock market return series display skewed distributions. Copyright © 2000 John Wiley & Sons, Ltd.     

Model averaging estimation for conditional volatility models with an application to stock market volatility forecast

This paper is concerned with model averaging estimation for conditional volatility models. Given a set of candidate models with different functional forms, we propose a model averaging estimator and forecast for conditional volatility, and construct the corresponding weight-choosing criterion. Under some regulatory conditions, we show that the weight selected by the criterion asymptotically minimizes the true Kullback–Leibler divergence, which is the distributional approximation error, as well as the Itakura–Saito distance, which is the distance between the true and estimated or forecast conditional volatility. Monte Carlo experiments support our newly proposed method. As for the empirical applications of our method, we investigate a total of nine major stock market indices and make a 1-day-ahead volatility forecast for each data set. Empirical results show that the model averaging forecast achieves the highest accuracy in terms of all types of loss functions in most cases, which captures the movement of the unknown true conditional volatility.     

Predictive ability and economic gains from volatility forecast combinations

The availability of numerous modeling approaches for volatility forecasting leads to model uncertainty for both researchers and practitioners. A large number of studies provide evidence in favor of combination methods for forecasting a variety of financial variables, but most of them are implemented on returns forecasting and evaluate their performance based solely on statistical evaluation criteria. In this paper, we combine various volatility forecasts based on different combination schemes and evaluate their performance in forecasting the volatility of the S&P 500 index. We use an exhaustive variety of combination methods to forecast volatility, ranging from simple techniques to time-varying techniques based on the past performance of the single models and regression techniques. We then evaluate the forecasting performance of single and combination volatility forecasts based on both statistical and economic loss functions. The empirical analysis in this paper yields an important conclusion. Although combination forecasts based on more complex methods perform better than the simple combinations and single models, there is no dominant combination technique that outperforms the rest in both statistical and economic terms.     

Performance of GARCH models in forecasting stock market volatility

This paper studies the performance of GARCH model and its modifications, using the rate of returns from the daily stock market indices of the Kuala Lumpur Stock Exchange (KLSE) including Composite Index, Tins Index, Plantations Index, Properties Index, and Finance Index. The models are stationary GARCH, unconstrained GARCH, non‐negative GARCH, GARCH‐M, exponential GARCH and integrated GARCH. The parameters of these models and variance processes are estimated jointly using the maximum likelihood method. The performance of the within‐sample estimation is diagnosed using several goodness‐of‐fit statistics. We observed that, among the models, even though exponential GARCH is not the best model in the goodness‐of‐fit statistics, it performs best in describing the often‐observed skewness in stock market indices and in out‐of‐sample (one‐step‐ahead) forecasting. The integrated GARCH, on the other hand, is the poorest model in both respects. Copyright © 1999 John Wiley & Sons, Ltd.     

Combining multivariate volatility forecasts using weighted losses

The ability to improve out-of-sample forecasting performance by combining forecasts is well established in the literature. This paper advances this literature in the area of multivariate volatility forecasts by developing two combination weighting schemes that exploit volatility persistence to emphasise certain losses within the combination estimation period. A comprehensive empirical analysis of the out-of-sample forecast performance across varying dimensions, loss functions, sub-samples and forecast horizons show that new approaches significantly outperform their counterparts in terms of statistical accuracy. Within the financial applications considered, significant benefits from combination forecasts relative to the individual candidate models are observed. Although the more sophisticated combination approaches consistently rank higher relative to the equally weighted approach, their performance is statistically indistinguishable given the relatively low power of these loss functions. Finally, within the applications, further analysis highlights how combination forecasts dramatically reduce the variability in the parameter of interest, namely the portfolio weight or beta.     

Forecasting exchange rate volatility: a multiple horizon comparison using historical,realized and implied volatility measures

Recent studies suggest realized volatility provides forecasts that are as good as option‐implied volatilities, with improvement stemming from the use of high‐frequency data instead of a long‐memory specification. This paper examines whether volatility persistence can be captured by a longer dataset consisting of over 15 years of intra‐day data. Volatility forecasts are evaluated using four exchange rates (AUD/USD, EUR/USD, GBP/USD, USD/JPY) over horizons ranging from 1 day to 3 months, using an expanded set of short‐range and long‐range dependence models. The empirical results provide additional evidence that significant incremental information is found in historical forecasts, beyond the implied volatility information for all forecast horizons. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting US GNP growth: The role of uncertainty

A large number of models have been developed in the literature to analyze and forecast changes in output dynamics. The objective of this paper was to compare the predictive ability of univariate and bivariate models, in terms of forecasting US gross national product (GNP) growth at different forecasting horizons, with the bivariate models containing information on a measure of economic uncertainty. Based on point and density forecast accuracy measures, as well as on equal predictive ability (EPA) and superior predictive ability (SPA) tests, we evaluate the relative forecasting performance of different model specifications over the quarterly period of 1919:Q2 until 2014:Q4. We find that the economic policy uncertainty (EPU) index should improve the accuracy of US GNP growth forecasts in bivariate models. We also find that the EPU exhibits similar forecasting ability to the term spread and outperforms other uncertainty measures such as the volatility index and geopolitical risk in predicting US recessions. While the Markov switching time‐varying parameter vector autoregressive model yields the lowest values for the root mean squared error in most cases, we observe relatively low values for the log predictive density score, when using the Bayesian vector regression model with stochastic volatility. More importantly, our results highlight the importance of uncertainty in forecasting US GNP growth rates.     

Forecasting volatility with noisy jumps: an application to the Dow Jones Industrial Average stocks

Empirical high‐frequency data can be used to separate the continuous and the jump components of realized volatility. This may improve on the accuracy of out‐of‐sample realized volatility forecasts. A further improvement may be realized by disentangling the two components using a sampling frequency at which the market microstructure effect is negligible, and this is the objective of the paper. In particular, a significant improvement in the accuracy of volatility forecasts is obtained by deriving the jump information from time intervals at which the noise effect is weak. Copyright © 2008 John Wiley & Sons, Ltd.     

A comparison of conditional predictive ability of implied volatility and realized measures in forecasting volatility

In a conditional predictive ability test framework, we investigate whether market factors influence the relative conditional predictive ability of realized measures (RMs) and implied volatility (IV), which is able to examine the asynchronism in their forecasting accuracy, and further analyze their unconditional forecasting performance for volatility forecast. Our results show that the asynchronism can be detected significantly and is strongly related to certain market factors, and the comparison between RMs and IV on average forecast performance is more efficient than previous studies. Finally, we use the factors to extend the empirical similarity (ES) approach for combination of forecasts derived from RMs and IV.     

Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors

In this paper, we assess the predictive content of latent economic policy uncertainty and data surprise factors for forecasting and nowcasting gross domestic product (GDP) using factor-type econometric models. Our analysis focuses on five emerging market economies: Brazil, Indonesia, Mexico, South Africa, and Turkey; and we carry out a forecasting horse race in which predictions from various different models are compared. These models may (or may not) contain latent uncertainty and surprise factors constructed using both local and global economic datasets. The set of models that we examine in our experiments includes both simple benchmark linear econometric models as well as dynamic factor models that are estimated using a variety of frequentist and Bayesian data shrinkage methods based on the least absolute shrinkage operator (LASSO). We find that the inclusion of our new uncertainty and surprise factors leads to superior predictions of GDP growth, particularly when these latent factors are constructed using Bayesian variants of the LASSO. Overall, our findings point to the importance of spillover effects from global uncertainty and data surprises, when predicting GDP growth in emerging market economies.     

Forecasting Errors,Directional Accuracy and Profitability of Currency Trading: The Case of EUR/USD Exchange Rate

We provide a comprehensive study of out‐of‐sample forecasts for the EUR/USD exchange rate based on multivariate macroeconomic models and forecast combinations. We use profit maximization measures based on directional accuracy and trading strategies in addition to standard loss minimization measures. When comparing predictive accuracy and profit measures, data snooping bias free tests are used. The results indicate that forecast combinations, in particular those based on principal components of forecasts, help to improve over benchmark trading strategies, although the excess return per unit of deviation is limited. Copyright © 2016 John Wiley & Sons, Ltd.