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.     

Out‐of‐sample volatility prediction: A new mixed‐frequency approach

This paper proposes a new mixed‐frequency approach to predict stock return volatilities out‐of‐sample. Based on the strategy of momentum of predictability (MoP), our mixed‐frequency approach has a model switching mechanism that switches between generalized autoregressive conditional heteroskedasticity (GARCH)‐class models that only use low‐frequency data and heterogeneous autoregressive models of realized volatility (HAR‐RV)‐type that only use high‐frequency data. The MoP model simply selects a forecast with relatively good past performance between the GARCH‐class and HAR‐RV‐type forecasts. The model confidence set (MCS) test shows that our MoP strategy significantly outperforms the competing models, which is robust to various settings. The MoP test shows that a relatively good recent past forecasting performance of the GARCH‐class or HAR‐RV‐type model is significantly associated with a relatively good current performance, supporting the success of the MoP model.     

Forecasting the Daily Time‐Varying Beta of European Banks During the Crisis Period: Comparison Between GARCH Models and the Kalman Filter

This intention of this paper is to empirically forecast the daily betas of a few European banks by means of four generalized autoregressive conditional heteroscedasticity (GARCH) models and the Kalman filter method during the pre‐global financial crisis period and the crisis period. The four GARCH models employed are BEKK GARCH, DCC GARCH, DCC‐MIDAS GARCH and Gaussian‐copula GARCH. The data consist of daily stock prices from 2001 to 2013 from two large banks each from Austria, Belgium, Greece, Holland, Ireland, Italy, Portugal and Spain. We apply the rolling forecasting method and the model confidence sets (MCS) to compare the daily forecasting ability of the five models during one month of the pre‐crisis (January 2007) and the crisis (January 2013) periods. Based on the MCS results, the BEKK proves the best model in the January 2007 period, and the Kalman filter overly outperforms the other models during the January 2013 period. Results have implications regarding the choice of model during different periods by practitioners and academics. Copyright © 2016 John Wiley & Sons, Ltd.     

Predicting the Distribution of Stock Returns: Model Formulation,Statistical Evaluation,VaR Analysis and Economic Significance

A large literature has investigated predictability of the conditional mean of low‐frequency stock returns by macroeconomic and financial variables; however, little is known about predictability of the conditional distribution. We look at one‐step‐ahead out‐of‐sample predictability of the conditional distribution of monthly US stock returns in relation to the macroeconomic and financial environment. Our methodological approach is innovative: we consider several specifications for the conditional density and combinations schemes. Our results are as follows: the entire density is predicted under combination schemes as applied to univariate GARCH models with Gaussian innovations; the Bayesian winner in relation to GARCH‐skewed‐t models is informative about the 5% value at risk; the average realised utility of a mean–variance investor is maximised under the Bayesian winner as applied to GARCH models with symmetric Student t innovations. Our results have two implications: the best prediction model depends on the evaluation criterion; and combination schemes outperform individual models. Copyright © 2015 John Wiley & Sons, Ltd.     

Gamma stochastic volatility models

This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The in‐sample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out‐of‐sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models. Copyright © 2006 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.     

On a dynamic mixture GARCH model

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non‐stationary volatility component. The VaR based on the new model performs better than traditional GARCH‐based VaRs, especially in unstable stock markets. Copyright © 2008 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.     

Bias in the estimation of non‐linear transformations of the integrated variance of returns

Volatility models such as GARCH, although misspecified with respect to the data‐generating process, may well generate volatility forecasts that are unconditionally unbiased. In other words, they generate variance forecasts that, on average, are equal to the integrated variance. However, many applications in finance require a measure of return volatility that is a non‐linear function of the variance of returns, rather than of the variance itself. Even if a volatility model generates forecasts of the integrated variance that are unbiased, non‐linear transformations of these forecasts will be biased estimators of the same non‐linear transformations of the integrated variance because of Jensen's inequality. In this paper, we derive an analytical approximation for the unconditional bias of estimators of non‐linear transformations of the integrated variance. This bias is a function of the volatility of the forecast variance and the volatility of the integrated variance, and depends on the concavity of the non‐linear transformation. In order to estimate the volatility of the unobserved integrated variance, we employ recent results from the realized volatility literature. As an illustration, we estimate the unconditional bias for both in‐sample and out‐of‐sample forecasts of three non‐linear transformations of the integrated standard deviation of returns for three exchange rate return series, where a GARCH(1, 1) model is used to forecast the integrated variance. Our estimation results suggest that, in practice, the bias can be substantial. Copyright © 2006 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.     

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

We study the performance of recently developed linear regression models for interval data when it comes to forecasting the uncertainty surrounding future stock returns. These interval data models use easy‐to‐compute daily return intervals during the modeling, estimation and forecasting stage. They have to stand up to comparable point‐data models of the well‐known capital asset pricing model type—which employ single daily returns based on successive closing prices and might allow for GARCH effects—in a comprehensive out‐of‐sample forecasting competition. The latter comprises roughly 1000 daily observations on all 30 stocks that constitute the DAX, Germany's main stock index, for a period covering both the calm market phase before and the more turbulent times during the recent financial crisis. The interval data models clearly outperform simple random walk benchmarks as well as the point‐data competitors in the great majority of cases. This result does not only hold when one‐day‐ahead forecasts of the conditional variance are considered, but is even more evident when the focus is on forecasting the width or the exact location of the next day's return interval. Regression models based on interval arithmetic thus prove to be a promising alternative to established point‐data volatility forecasting tools. Copyright ©2015 John Wiley & Sons, Ltd.     

Prediction of α‐stable GARCH and ARMA‐GARCH‐M models

The best prediction of generalized autoregressive conditional heteroskedasticity (GARCH) models with α‐stable innovations, α‐stable power‐GARCH models and autoregressive moving average (ARMA) models with GARCH in mean effects (ARMA‐GARCH‐M) are proposed. We present a sufficient condition for stationarity of α‐stable GARCH models. The prediction methods are easy to implement in practice. The proposed prediction methods are applied for predicting future values of the daily SP500 stock market and wind speed data.     

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.     

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.     

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.     

Term Structure Forecasting of Government Bond Yields with Latent and Macroeconomic Factors: Do Macroeconomic Factors Imply Better Out‐of‐Sample Forecasts?

This study empirically examines the role of macroeconomic and stock market variables in the dynamic Nelson–Siegel framework with the purpose of fitting and forecasting the term structure of interest rate on the Japanese government bond market. The Nelson–Siegel type models in state‐space framework considerably outperform the benchmark simple time series forecast models such as an AR(1) and a random walk. The yields‐macro model incorporating macroeconomic factors leads to a better in‐sample fit of the term structure than the yields‐only model. The out‐of‐sample predictability of the former for short‐horizon forecasts is superior to the latter for all maturities examined in this study, and for longer horizons the former is still compatible to the latter. Inclusion of macroeconomic factors can dramatically reduce the autocorrelation of forecast errors, which has been a common phenomenon of statistical analysis in previous term structure models. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling and Forecasting the Yield Curve by an Extended Nelson‐Siegel Class of Models: A Quantile Autoregression Approach

This paper compares the in‐sample fitting and the out‐of‐sample forecasting performances of four distinct Nelson–Siegel class models: Nelson–Siegel, Bliss, Svensson, and a five‐factor model we propose in order to enhance the fitting flexibility. The introduction of the fifth factor resulted in superior adjustment to the data. For the forecasting exercise the paper contrasts the performances of the term structure models in association with the following econometric methods: quantile autoregression evaluated at the median, VAR, AR, and a random walk. As a pattern, the quantile procedure delivered the best results for longer forecasting horizons. Copyright © 2011 John Wiley & Sons, Ltd.     

International equity flows and the predictability of US stock returns

We examined the link between international equity flows and US stock returns. Based on the results of tests of in‐sample and out‐of‐sample predictability of stock returns, we found evidence of a strong positive (negative) link between international equity flows and contemporaneous (one‐month‐ahead) stock returns. Our results also indicate that an investor, in real time, could have used information on the link between international equity flows and one‐month‐ahead stock returns to improve the performance of simple trading rules. Copyright © 2007 John Wiley & Sons, Ltd.     

Parsimonious modeling and forecasting of corporate yield curve

This paper investigates the sensitivity of out‐of‐sample forecasting performance over a span of different parameters of l in the dynamic Nelson–Siegel three‐factor AR(1) model. First, we find that the ad hoc selection of l is not optimal. Second, we find a substantial difference in factor dynamics between investment‐grade and speculative‐grade corporate bonds from 1994:12 to 2006: 4. Third, we suggest that the three‐factor model is sufficient to explain the main variations of corporate yield changes. Finally, the parsimonious Nelson–Siegel three‐factor AR(1) model remains competitive in the out‐of‐sample forecasting of corporate yields. Copyright © 2008 John Wiley & Sons, Ltd.     

The performance of non‐linear exchange rate models: a forecasting comparison

In recent years there has been a considerable development in modelling non‐linearities and asymmetries in economic and financial variables. The aim of the current paper is to compare the forecasting performance of different models for the returns of three of the most traded exchange rates in terms of the US dollar, namely the French franc (FF/$), the German mark (DM/$) and the Japanese yen (Y/$). The relative performance of non‐linear models of the SETAR, STAR and GARCH types is contrasted with their linear counterparts. The results show that if attention is restricted to mean square forecast errors, the performance of the models, when distinguishable, tends to favour the linear models. The forecast performance of the models is evaluated also conditional on the regime at the forecast origin and on density forecasts. This analysis produces more evidence of forecasting gains from non‐linear models. Copyright © 2002 John Wiley & Sons, Ltd.