Forecasting Volatility with Many Predictors

This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian Forecasting for Financial Risk Management,Pre and Post the Global Financial Crisis

Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Daily volatility forecasts: reassessing the performance of GARCH models

Volatility plays a key role in asset and portfolio management and derivatives pricing. As such, accurate measures and good forecasts of volatility are crucial for the implementation and evaluation of asset and derivative pricing models in addition to trading and hedging strategies. However, whilst GARCH models are able to capture the observed clustering effect in asset price volatility in‐sample, they appear to provide relatively poor out‐of‐sample forecasts. Recent research has suggested that this relative failure of GARCH models arises not from a failure of the model but a failure to specify correctly the ‘true volatility’ measure against which forecasting performance is measured. It is argued that the standard approach of using ex post daily squared returns as the measure of ‘true volatility’ includes a large noisy component. An alternative measure for ‘true volatility’ has therefore been suggested, based upon the cumulative squared returns from intra‐day data. This paper implements that technique and reports that, in a dataset of 17 daily exchange rate series, the GARCH model outperforms smoothing and moving average techniques which have been previously identified as providing superior volatility forecasts. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal sampling frequency for volatility forecast models for the Indian stock markets

This paper evaluates the performance of conditional variance models using high‐frequency data of the National Stock Index (S&P CNX NIFTY) and attempts to determine the optimal sampling frequency for the best daily volatility forecast. A linear combination of the realized volatilities calculated at two different frequencies is used as benchmark to evaluate the volatility forecasting ability of the conditional variance models (GARCH (1, 1)) at different sampling frequencies. From the analysis, it is found that sampling at 30 minutes gives the best forecast for daily volatility. The forecasting ability of these models is deteriorated, however, by the non‐normal property of mean adjusted returns, which is an assumption in conditional variance models. Nevertheless, the optimum frequency remained the same even in the case of different models (EGARCH and PARCH) and different error distribution (generalized error distribution, GED) where the error is reduced to a certain extent by incorporating the asymmetric effect on volatility. Our analysis also suggests that GARCH models with GED innovations or EGRACH and PARCH models would give better estimates of volatility with lower forecast error estimates. Copyright © 2008 John Wiley & Sons, Ltd.     

Empirical analysis and forecasting of volatility dynamics in high‐frequency returns with time‐varying components

We study intraday return volatility dynamics using a time‐varying components approach, and the method is applied to analyze IBM intraday returns. Empirical evidence indicates that with three additive components—a time‐varying mean of absolute returns and two cosine components with time‐varying amplitudes—together they capture very well the pronounced periodicity and persistence behaviors exhibited in the empirical autocorrelation pattern of IBM returns. We find that the long‐run volatility persistence is driven predominantly by daily level shifts in mean absolute returns. After adjusting for these intradaily components, the filtered returns behave much like a Gaussian noise, suggesting that the three‐components structure is adequately specified. Furthermore, a new volatility measure (TCV) can be constructed from these components. Results from extensive out‐of‐sample rolling forecast experiments suggest that TCV fares well in predicting future volatility against alternative methods, including GARCH model, realized volatility and realized absolute value. Copyright © 2009 John Wiley & Sons, Ltd.     

A Bayesian threshold nonlinearity test for financial time series

We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd.     

Daily FX Volatility Forecasts: Can the GARCH(1,1) Model be Beaten using High‐Frequency Data?

Volatility forecasting remains an active area of research with no current consensus as to the model that provides the most accurate forecasts, though Hansen and Lunde (2005) have argued that in the context of daily exchange rate returns nothing can beat a GARCH(1,1) model. This paper extends that line of research by utilizing intra‐day data and obtaining daily volatility forecasts from a range of models based upon the higher‐frequency data. The volatility forecasts are appraised using four different measures of ‘true’ volatility and further evaluated using regression tests of predictive power, forecast encompassing and forecast combination. Our results show that the daily GARCH(1,1) model is largely inferior to all other models, whereas the intra‐day unadjusted‐data GARCH(1,1) model generally provides superior forecasts compared to all other models. Hence, while it appears that a daily GARCH(1,1) model can be beaten in obtaining accurate daily volatility forecasts, an intra‐day GARCH(1,1) model cannot be. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting commodity prices: GARCH,jumps, and mean reversion

In examining stochastic models for commodity prices, central questions often revolve around time‐varying trend, stochastic convenience yield and volatility, and mean reversion. This paper seeks to assess and compare alternative approaches to modelling these effects, with focus on forecast performance. Three specifications are considered: (i) random‐walk models with GARCH and normal or Student‐t innovations; (ii) Poisson‐based jump‐diffusion models with GARCH and normal or Student‐t innovations; and (iii) mean‐reverting models that allow for uncertainty in equilibrium price. Our empirical application makes use of aluminium spot and futures price series at daily and weekly frequencies. Results show: (i) models with stochastic convenience yield outperform all other competing models, and for all forecast horizons; (ii) the use of futures prices does not always yield lower forecast error values compared to the use of spot prices; and (iii) within the class of (G)ARCH random‐walk models, no model uniformly dominates the other. Copyright © 2008 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.     

Volatility forecasting with double Markov switching GARCH models

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat‐tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first‐order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value‐at‐risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.     

Are industry‐level indicators more helpful to forecast industrial stock volatility? Evidence from Chinese manufacturing purchasing managers index

Effectively explaining and accurately forecasting industrial stock volatility can provide crucial references to develop investment strategies, prevent market risk and maintain the smooth running of national economy. This paper aims to discuss the roles of industry‐level indicators in industrial stock volatility. Selecting Chinese manufacturing purchasing managers index (PMI) and its five component PMI as the proxies of industry‐level indicators, we analyze the contributions of PMI on industrial stock volatility and further compare the volatility forecasting performances of PMI, macroeconomic fundamentals and economic policy uncertainty (EPU), by constructing the individual and combination GARCH‐MIDAS models. The empirical results manifest that, first, most of the PMI has significant negative effects on industrial stock volatility. Second, PMI which focuses on the industrial sector itself is more helpful to forecast industrial stock volatility compared with the commonly used macroeconomic fundamentals and economic policy uncertainty. Finally, the combination GARCH‐MIDAS approaches based on DMA technique demonstrate more excellent predictive abilities than the individual GARCH‐MIDAS models. Our major conclusions are robust through various robustness checks.     

Garch forecasting performance under different distribution assumptions

This paper investigates the forecasting performance of the Garch (1, 1) model when estimated with NINE different error distributions on Standard and Poor's 500 Index Future returns. By utilizing the theory of realized variance to construct an appropriate ex post measure of volatility from intra‐day data it is shown that allowing for a leptokurtic error distribution leads to significant improvements in variance forecasts compared to using the normal distribution. This result holds for daily, weekly as well as monthly forecast horizons. It is also found that allowing for skewness and time variation in the higher moments of the distribution does not further improve forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Forecasting volatility by means of threshold models

The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out‐of‐sample forecasting ability of the SETAR‐Threshold GARCH (SETAR‐TGARCH) and the SETAR‐Threshold Stochastic Volatility (SETAR‐THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ‘true’ underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR‐THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves. Copyright © 2007 John Wiley & Sons, Ltd.     

An outlier robust GARCH model and forecasting volatility of exchange rate returns

Since volatility is perceived as an explicit measure of risk, financial economists have long been concerned with accurate measures and forecasts of future volatility and, undoubtedly, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model has been widely used for doing so. It appears, however, from some empirical studies that the GARCH model tends to provide poor volatility forecasts in the presence of additive outliers. To overcome the forecasting limitation, this paper proposes a robust GARCH model (RGARCH) using least absolute deviation estimation and introduces a valuable estimation method from a practical point of view. Extensive Monte Carlo experiments substantiate our conjectures. As the magnitude of the outliers increases, the one‐step‐ahead forecasting performance of the RGARCH model has a more significant improvement in two forecast evaluation criteria over both the standard GARCH and random walk models. Strong evidence in favour of the RGARCH model over other competitive models is based on empirical application. By using a sample of two daily exchange rate series, we find that the out‐of‐sample volatility forecasts of the RGARCH model are apparently superior to those of other competitive models. Copyright © 2002 John Wiley & Sons, Ltd.     

A Double‐threshold GARCH Model for the French Franc/Deutschmark exchange rate

This paper combines and generalizes a number of recent time series models of daily exchange rate series by using a SETAR model which also allows the variance equation of a GARCH specification for the error terms to be drawn from more than one regime. An application of the model to the French Franc/Deutschmark exchange rate demonstrates that out‐of‐sample forecasts for the exchange rate volatility are also improved when the restriction that the data it is drawn from a single regime is removed. This result highlights the importance of considering both types of regime shift (i.e. thresholds in variance as well as in mean) when analysing financial time series. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

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.     

Comparison of forecasting performances: Does normalization and variance stabilization method beat GARCH(1,1)‐type models? Empirical evidence from the stock markets

In this paper, we present a comparison between the forecasting performances of the normalization and variance stabilization method (NoVaS) and the GARCH(1,1), EGARCH(1,1) and GJR‐GARCH(1,1) models. Hence the aim of this study is to compare the out‐of‐sample forecasting performances of the models used throughout the study and to show that the NoVaS method is better than GARCH(1,1)‐type models in the context of out‐of sample forecasting performance. We study the out‐of‐sample forecasting performances of GARCH(1,1)‐type models and NoVaS method based on generalized error distribution, unlike normal and Student's t‐distribution. Also, what makes the study different is the use of the return series, calculated logarithmically and arithmetically in terms of forecasting performance. For comparing the out‐of‐sample forecasting performances, we focused on different datasets, such as S&P 500, logarithmic and arithmetic B?ST 100 return series. The key result of our analysis is that the NoVaS method performs better out‐of‐sample forecasting performance than GARCH(1,1)‐type models. The result can offer useful guidance in model building for out‐of‐sample forecasting purposes, aimed at improving forecasting accuracy.     

The Volatility and Density Prediction Performance of Alternative GARCH Models

This study compares the volatility and density prediction performance of alternative GARCH models with different conditional distribution specifications. The conditional residuals are specified as normal, skewedHyphen;t or compound Poisson (jump) distribution based upon a nonlinear and asymmetric GARCH (NGARCH) model framework. The empirical results for the S&P 500 and FTSE 100 index returns suggest that the jump model outperforms all other models in terms of both volatility forecasting and density prediction. Nevertheless, the superiority of the nonHyphen;normal models is not always significant and diminished during the sample period on those occasions when volatility experiences an obvious structural change. Copyright © 2011 John Wiley & Sons, Ltd.