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GARCH Models (garch + models)
Kinds of GARCH Models Selected AbstractsAssessing the Forecasting Performance of Regime-Switching, ARIMA and GARCH Models of House PricesREAL ESTATE ECONOMICS, Issue 2 2003Gordon W. Crawford While price changes on any particular home are difficult to predict, aggregate home price changes are forecastable. In this context, this paper compares the forecasting performance of three types of univariate time series models: ARIMA, GARCH and regime-switching. The underlying intuition behind regime-switching models is that the series of interest behaves differently depending on the realization of an unobservable regime variable. Regime-switching models are a compelling choice for real estate markets that have historically displayed boom and bust cycles. However, we find that, while regime-switching models can perform better in-sample, simple ARIMA models generally perform better in out-of-sample forecasting. [source] Deterministic and Stochastic Methods for Estimation of Intra-day Seasonal Components with High Frequency DataECONOMIC NOTES, Issue 2 2001Andrea Beltratti We introduce a model for the analysis of intra-day volatility based on unobserved components. The stochastic seasonal component is essential to model time-varing intra-day effects. The model is estimated with high frequency data for Deutsche mark,US dollar for 1993 and 1996. The model performs well in terms of coherence with the theoretical aggregation properties of GARCH models, it is effective in terms of both forecasting ability and describing reactions to macroeconomic news. (J.E.L.: C14, C53, F31). [source] Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary SystemFINANCIAL REVIEW, Issue 1 2000Colm Kearney C32/F31/G15 Abstract We construct a series of 3-, 4- and 5-variable multivariate GARCH models of exchange rate volatility transmission across the important European Monetary System (EMS) currencies including the French franc, the German mark, the Italian lira, and the European Currency Unit. The models are estimated without imposing the common restriction of constant correlation on both daily and weekly data from April 1979,March 1997. Our results indicate the importance of checking for specification robustness in multivariate Generalized Autoregressive Conditional Heleroskedasticity (GARCH) modeling, we find that increased temporal aggregation reduces observed volatility transmission, and that the mark plays a dominant position in terms of volatility transmission. [source] Forecasting financial volatility of the Athens stock exchange daily returns: an application of the asymmetric normal mixture GARCH modelINTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 4 2010Anastassios A. Drakos Abstract In this paper we model the return volatility of stocks traded in the Athens Stock Exchange using alternative GARCH models. We employ daily data for the period January 1998 to November 2008 allowing us to capture possible positive and negative effects that may be due to either contagion or idiosyncratic sources. The econometric analysis is based on the estimation of a class of five GARCH models under alternative assumptions with respect to the error distribution. The main findings of our analysis are: first, based on a battery of diagnostic tests it is shown that the normal mixture asymmetric GARCH (NM-AGARCH) models perform better in modeling the volatility of stock returns. Second, it is shown that with the use of the Kupiec's tests for in-sample and out-of-sample forecasting performance the evidence is mixed as the choice of the appropriate volatility model depends on the trading position under consideration. Third, at the 99% confidence interval the NM-AGARCH model with skewed Student-distribution outperforms all other competing models both for in-sample and out-of-sample forecasting performance. This increase in predictive performance for higher confidence intervals of the NM-AGARCH model with skewed Student-distribution makes this specification consistent with the requirements of the Basel II agreement. Copyright © 2010 John Wiley & Sons, Ltd. [source] Realising the future: forecasting with high-frequency-based volatility (HEAVY) modelsJOURNAL OF APPLIED ECONOMETRICS, Issue 2 2010Professor Neil Shephard This paper studies in some detail a class of high-frequency-based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realised measures constructed from high-frequency data. Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process. We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models. We analyse a model-based bootstrap which allows us to estimate the entire predictive distribution of returns. We also provide an analysis of missing data in the context of these models. Copyright © 2010 John Wiley & Sons, Ltd. [source] Normal mixture GARCH(1,1): applications to exchange rate modellingJOURNAL OF APPLIED ECONOMETRICS, Issue 3 2006Carol Alexander Some recent specifications for GARCH error processes explicitly assume a conditional variance that is generated by a mixture of normal components, albeit with some parameter restrictions. This paper analyses the general normal mixture GARCH(1,1) model which can capture time variation in both conditional skewness and kurtosis. A main focus of the paper is to provide evidence that, for modelling exchange rates, generalized two-component normal mixture GARCH(1,1) models perform better than those with three or more components, and better than symmetric and skewed Student's t -GARCH models. In addition to the extensive empirical results based on simulation and on historical data on three US dollar foreign exchange rates (British pound, euro and Japanese yen), we derive: expressions for the conditional and unconditional moments of all models; parameter conditions to ensure that the second and fourth conditional and unconditional moments are positive and finite; and analytic derivatives for the maximum likelihood estimation of the model parameters and standard errors of the estimates. Copyright © 2006 John Wiley & Sons, Ltd. [source] Supply response and price volatility in the Greek broiler marketAGRIBUSINESS : AN INTERNATIONAL JOURNAL, Issue 1 2010Anthony N. Rezitis The authors examine the supply response of the Greek broiler market. A generalized autoregressive conditional heteroskedasticity (GARCH) process is used to estimate expected price and price volatility; price and supply equations are estimated jointly. In addition to the standard GARCH model, several different symmetric, asymmetric, and nonlinear GARCH models are estimated. These models use different conditional variance specifications (linear or nonlinear) to grasp some additional empirical regularity of data like asymmetry. Asymmetric price volatility means that different volatility is recorded in the case of a fall in prices than an increase in prices by the same amount. The possible existence of asymmetry in the producer's price volatility gives useful information about market structure and possible market power. The empirical results indicate that among the estimated GARCH models the nonlinear asymmetric GARCH model (NAGARCH) seems to better describe producers' price volatility of the Greek broiler industry. Furthermore, the empirical findings show that price volatility is an important risk factor and broiler feed price is the most significant cost factor of the supply response function. Finally, the model provides forecasts for quantity supplied, producers' price, and price volatility. [EconLit. Classifications: Q110, C510, D200]. © 2010 Wiley Periodicals, Inc. [source] Volatility forecasting with double Markov switching GARCH modelsJOURNAL OF FORECASTING, Issue 8 2009Cathy W. S. Chen Abstract 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. [source] Optimal sampling frequency for volatility forecast models for the Indian stock marketsJOURNAL OF FORECASTING, Issue 1 2009Malay Bhattacharyya Abstract 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. [source] Evaluation of correlation forecasting models for risk managementJOURNAL OF FORECASTING, Issue 7 2007Vasiliki D. Skintzi Abstract Reliable correlation forecasts are of paramount importance in modern risk management systems. A plethora of correlation forecasting models have been proposed in the open literature, yet their impact on the accuracy of value-at-risk calculations has not been explicitly investigated. In this paper, traditional and modern correlation forecasting techniques are compared using standard statistical and risk management loss functions. Three portfolios consisting of stocks, bonds and currencies are considered. We find that GARCH models can better account for the correlation's dynamic structure in the stock and bond portfolios. On the other hand, simpler specifications such as the historical mean model or simple moving average models are better suited for the currency portfolio.,,Copyright © 2007 John Wiley & Sons, Ltd. [source] Average conditional correlation and tree structures for multivariate GARCH modelsJOURNAL OF FORECASTING, Issue 8 2006Francesco Audrino Abstract We propose a simple class of multivariate GARCH models, allowing for time-varying conditional correlations. Estimates for time-varying conditional correlations are constructed by means of a convex combination of averaged correlations (across all series) and dynamic realized (historical) correlations. Our model is very parsimonious. Estimation is computationally feasible in very large dimensions without resorting to any variance reduction technique. We back-test the models on a six-dimensional exchange-rate time series using different goodness-of-fit criteria and statistical tests. We collect empirical evidence of their strong predictive power, also in comparison to alternative benchmark procedures.,,Copyright © 2006 John Wiley & Sons, Ltd. [source] A Bayesian threshold nonlinearity test for financial time seriesJOURNAL OF FORECASTING, Issue 1 2005Mike K. P. So Abstract 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. [source] Value at risk from econometric models and implied from currency optionsJOURNAL OF FORECASTING, Issue 8 2004James ChongArticle first published online: 3 DEC 200 Abstract This paper compares daily exchange rate value at risk estimates derived from econometric models with those implied by the prices of traded options. Univariate and multivariate GARCH models are employed in parallel with the simple historical and exponentially weighted moving average methods. Overall, we find that during periods of stability, the implied model tends to overestimate value at risk, hence over-allocating capital. However, during turbulent periods, it is less responsive than the GARCH-type models, resulting in an under-allocation of capital and a greater number of failures. Hence our main conclusion, which has important implications for risk management, is that market expectations of future volatility and correlation, as determined from the prices of traded options, may not be optimal tools for determining value at risk. Therefore, alternative models for estimating volatility should be sought. Copyright © 2004 John Wiley & Sons, Ltd. [source] Daily volatility forecasts: reassessing the performance of GARCH modelsJOURNAL OF FORECASTING, Issue 6 2004David G. McMillan Abstract 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. [source] APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICINGMATHEMATICAL FINANCE, Issue 1 2006Jin-Chuan Duan This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored. [source] Modelling Regime-Specific Stock Price Volatility,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 6 2009Carol Alexander Abstract Single-state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state-dependent behaviour of volatility nor explain why the equity index skew persists into long-dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state-dependent leverage effect to NM-GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time-varying volatility risk premia. An empirical study on European equity indices identifies two-state asymmetric NM-GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean-reversion and leverage effects during crash markets are quite different from those in the stable regime. [source] Dynamic hedging with futures: A copula-based GARCH modelTHE JOURNAL OF FUTURES MARKETS, Issue 11 2008Chih-Chiang Hsu In a number of earlier studies it has been demonstrated that the traditional regression-based static approach is inappropriate for hedging with futures, with the result that a variety of alternative dynamic hedging strategies have emerged. In this study the authors propose a class of new copula-based GARCH models for the estimation of the optimal hedge ratio and compare their effectiveness with that of other hedging models, including the conventional static, the constant conditional correlation (CCC) GARCH, and the dynamic conditional correlation (DCC) GARCH models. With regard to the reduction of variance in the returns of hedged portfolios, the empirical results show that in both the in-sample and out-of-sample tests, with full flexibility in the distribution specifications, the copula-based GARCH models perform more effectively than other dynamic hedging models. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1095,1116, 2008 [source] A simplified approach to modeling the co-movement of asset returnsTHE JOURNAL OF FUTURES MARKETS, Issue 6 2007Richard D. F. Harris The authors propose a simplified multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model (the S-GARCH model), which involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The proposed model is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. The S-GARCH model is used to estimate the minimum-variance hedge ratio for the FTSE (Financial Times and the London Stock Exchange) 100 Index portfolio, hedged using index futures, and compared to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, it was found that the S-GARCH model performs at least as well as the other models that were considered, and in some cases it was better. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:575,598, 2007 [source] APPROXIMATING VOLATILITIES BY ASYMMETRIC POWER GARCH FUNCTIONSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009Jeremy Penzer Summary ARCH/GARCH representations of financial series usually attempt to model the serial correlation structure of squared returns. Although it is undoubtedly true that squared returns are correlated, there is increasing empirical evidence of stronger correlation in the absolute returns than in squared returns. Rather than assuming an explicit form for volatility, we adopt an approximation approach; we approximate the ,th power of volatility by an asymmetric GARCH function with the power index , chosen so that the approximation is optimum. Asymptotic normality is established for both the quasi-maximum likelihood estimator (qMLE) and the least absolute deviations estimator (LADE) in our approximation setting. A consequence of our approach is a relaxation of the usual stationarity condition for GARCH models. In an application to real financial datasets, the estimated values for , are found to be close to one, consistent with the stylized fact that the strongest autocorrelation is found in the absolute returns. A simulation study illustrates that the qMLE is inefficient for models with heavy-tailed errors, whereas the LADE is more robust. [source] | ||||||||||||||||||||||