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 value‐at‐risk with a parsimonious portfolio spillover GARCH (PS‐GARCH) model

Accurate modelling of volatility (or risk) is important in finance, particularly as it relates to the modelling and forecasting of value‐at‐risk (VaR) thresholds. As financial applications typically deal with a portfolio of assets and risk, there are several multivariate GARCH models which specify the risk of one asset as depending on its own past as well as the past behaviour of other assets. Multivariate effects, whereby the risk of a given asset depends on the previous risk of any other asset, are termed spillover effects. In this paper we analyse the importance of considering spillover effects when forecasting financial volatility. The forecasting performance of the VARMA‐GARCH model of Ling and McAleer (2003), which includes spillover effects from all assets, the CCC model of Bollerslev (1990), which includes no spillovers, and a new Portfolio Spillover GARCH (PS‐GARCH) model, which accommodates aggregate spillovers parsimoniously and hence avoids the so‐called curse of dimensionality, are compared using a VaR example for a portfolio containing four international stock market indices. The empirical results suggest that spillover effects are statistically significant. However, the VaR threshold forecasts are generally found to be insensitive to the inclusion of spillover effects in any of the multivariate models considered. Copyright © 2008 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.     

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.     

Model Uncertainty and Forecast Combination in High‐Dimensional Multivariate Volatility Prediction

In multivariate volatility prediction, identifying the optimal forecasting model is not always a feasible task. This is mainly due to the curse of dimensionality typically affecting multivariate volatility models. In practice only a subset of the potentially available models can be effectively estimated, after imposing severe constraints on the dynamic structure of the volatility process. It follows that in most applications the working forecasting model can be severely misspecified. This situation leaves scope for the application of forecast combination strategies as a tool for improving the predictive accuracy. The aim of the paper is to propose some alternative combination strategies and compare their performances in forecasting high‐dimensional multivariate conditional covariance matrices for a portfolio of US stock returns. In particular, we will consider the combination of volatility predictions generated by multivariate GARCH models, based on daily returns, and dynamic models for realized covariance matrices, built from intra‐daily returns. Copyright © 2015 John Wiley & Sons, Ltd.     

The Role of High‐Frequency Intra‐daily Data,Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting

This paper assesses the informational content of alternative realized volatility estimators, daily range and implied volatility in multi‐period out‐of‐sample Value‐at‐Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed Student's t distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi‐period VaR estimates. Our empirical findings, based on the S&P 500 stock index, indicate that almost all realized and implied volatility measures can produce statistically and regulatory precise VaR forecasts across forecasting horizons, with the implied volatility being especially accurate in monthly VaR forecasts. The daily range produces inferior forecasting results in terms of regulatory accuracy and Basel II compliance. However, robust realized volatility measures, which are immune against microstructure noise bias or price jumps, generate superior VaR estimates in terms of capital efficiency, as they minimize the opportunity cost of capital and the Basel II regulatory capital. Copyright © 2013 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.     

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.     

Factor Models of Stock Returns: GARCH Errors versus Time‐Varying Betas

This paper investigates the implications of time‐varying betas in factor models for stock returns. It is shown that a single‐factor model (SFMT) with autoregressive betas and homoscedastic errors (SFMT‐AR) is capable of reproducing the most important stylized facts of stock returns. An empirical study on the major US stock market sectors shows that SFMT‐AR outperforms, in terms of in‐sample and out‐of‐sample performance, SFMT with constant betas and conditionally heteroscedastic (GARCH) errors, as well as two multivariate GARCH‐type models. Copyright © 2016 John Wiley & Sons, Ltd.     

Improving Hull and White's Method of Estimating Portfolio Value‐at‐Risk

We propose a method approach. We use six international stock price indices and three hypothetical portfolios formed by these indices. The sample was observed daily from 1 January 1996 to 31 December 2006. Confirmed by the failure rates and backtesting developed by Kupiec (Technique for verifying the accuracy of risk measurement models. Journal of Derivatives 1995; 3 : 73–84) and Christoffersen (Evaluating interval forecasts. International Economic Review 1998; 39 : 841–862), the empirical results show that our method can considerably improve the estimation accuracy of value‐at‐risk. Thus the study establishes an effective alternative model for risk prediction and hence also provides a reliable tool for the management of portfolios. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models

We evaluate forecasting models of US business fixed investment spending growth over the recent 1995:1–2004:2 out‐of‐sample period. The forecasting models are based on the conventional Accelerator, Neoclassical, Average Q, and Cash‐Flow models of investment spending, as well as real stock prices and excess stock return predictors. The real stock price model typically generates the most accurate forecasts, and forecast‐encompassing tests indicate that this model contains most of the information useful for forecasting investment spending growth relative to the other models at longer horizons. In a robustness check, we also evaluate the forecasting performance of the models over two alternative out‐of‐sample periods: 1975:1–1984:4 and 1985:1–1994:4. A number of different models produce the most accurate forecasts over these alternative out‐of‐sample periods, indicating that while the real stock price model appears particularly useful for forecasting the recent behavior of investment spending growth, it may not continue to perform well in future periods. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluating volatility dynamics and the forecasting ability of Markov switching models

This paper uses Markov switching models to capture volatility dynamics in exchange rates and to evaluate their forecasting ability. We identify that increased volatilities in four euro‐based exchange rates are due to underlying structural changes. Also, we find that currencies are closely related to each other, especially in high‐volatility periods, where cross‐correlations increase significantly. Using Markov switching Monte Carlo approach we provide evidence in favour of Markov switching models, rejecting random walk hypothesis. Testing in‐sample and out‐of‐sample Markov trading rules based on Dueker and Neely (Journal of Banking and Finance, 2007) we find that using econometric methodology is able to forecast accurately exchange rate movements. When applied to the Euro/US dollar and the euro/British pound daily returns data, the model provides exceptional out‐of‐sample returns. However, when applied to the euro/Brazilian real and the euro/Mexican peso, the model loses power. Higher volatility exercised in the Latin American currencies seems to be a critical factor for this failure. Copyright © 2009 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.     

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.     

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.     

Non‐linear forecasts of stock returns

Following recent non‐linear extensions of the present‐value model, this paper examines the out‐of‐sample forecast performance of two parametric and two non‐parametric nonlinear models of stock returns. The parametric models include the standard regime switching and the Markov regime switching, whereas the non‐parametric are the nearest‐neighbour and the artificial neural network models. We focused on the US stock market using annual observations spanning the period 1872–1999. Evaluation of forecasts was based on two criteria, namely forecast accuracy and forecast encompassing. In terms of accuracy, the Markov and the artificial neural network models produce at least as accurate forecasts as the other models. In terms of encompassing, the Markov model outperforms all the others. Overall, both criteria suggest that the Markov regime switching model is the most preferable non‐linear empirical extension of the present‐value model for out‐of‐sample stock return forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

Does a lot help a lot? Forecasting stock returns with pooling strategies in a data‐rich environment

A variety of recent studies provide a skeptical view on the predictability of stock returns. Empirical evidence shows that most prediction models suffer from a loss of information, model uncertainty, and structural instability by relying on low‐dimensional information sets. In this study, we evaluate the predictive ability of various lately refined forecasting strategies, which handle these issues by incorporating information from many potential predictor variables simultaneously. We investigate whether forecasting strategies that (i) combine information and (ii) combine individual forecasts are useful to predict US stock returns, that is, the market excess return, size, value, and the momentum premium. Our results show that methods combining information have remarkable in‐sample predictive ability. However, the out‐of‐sample performance suffers from highly volatile forecast errors. Forecast combinations face a better bias–efficiency trade‐off, yielding a consistently superior forecast performance for the market excess return and the size premium even after the 1970s.     

Forecasting Daily Variations of Stock Index Returns with a Multifractal Model of Realized Volatility

Multifractal models have recently been introduced as a new type of data‐generating process for asset returns and other financial data. Here we propose an adaptation of this model for realized volatility. We estimate this new model via generalized method of moments and perform forecasting by means of best linear forecasts derived via the Levinson–Durbin algorithm. Its out‐of‐sample performance is compared against other popular time series specifications. Using an intra‐day dataset for five major international stock market indices, we find that the the multifractal model for realized volatility improves upon forecasts of its earlier counterparts based on daily returns and of many other volatility models. While the more traditional RV‐ARFIMA model comes out as the most successful model (in terms of the number of cases in which it has the best forecasts for all combinations of forecast horizons and evaluation criteria), the new model performs often significantly better during the turbulent times of the recent financial crisis. Copyright © 2014 John Wiley & Sons, Ltd.     

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.