Misspecification of Variants of autoregressive GARCH Models and Effect on In-Sample Forecasting (original) (raw)

A forecast comparison of volatility models: does anything beat a GARCH (1,1)?

2005

Abstract We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM–$ exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH (1, 1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH (1, 1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns.

Estimating stock market volatility using asymmetric GARCH models

Applied Financial Economics, 2008

A comprehensive empirical analysis of the mean return and conditional variance of Tel Aviv Stock Exchange (TASE) indices is performed using various GARCH models. The prediction performance of these conditional changing variance models is compared to newer asymmetric GJR and APARCH models. We also quantify the day-of-the-week effect and the leverage effect and test for asymmetric volatility. Our results show that the asymmetric GARCH model with fat-tailed densities improves overall estimation for measuring conditional variance. The EGARCH model using a skewed Student-t distribution is the most successful for forecasting TASE indices.

Evaluating the Volatility Forecasting Performance of Best Fitting GARCH Models in Emerging Asian Stock Markets

International Journal of Mathematics and Statistics, 2012

Problem statement : While modeling the volatility of returns is essential for many areas of finance, it is well known that financial return series exhibit many non-normal characteristics that cannot be captured by the standard GARCH model with a normal error distribution. But which GARCH model and which error distribution to use is still open to question, especially where the model that best fits the in-sample data may not give the most effective out-of-sample volatility forecasting ability. Approach: In this study, six simulated studies in GARCH(p,q) with six different error distributions are carried out. In each case, we determine the best fitting GARCH model based on the AIC criterion and then evaluate its outof-sample volatility forecasting performance against that of other models. The analysis is then carried out using the daily closing price data from Thailand (SET), Malaysia (KLCI) and Singapore (STI) stock exchanges. Results : Our simulations show that although the best fitting model does not always provide the best future volatility estimates the differences are so insignificant that the estimates of the best fitting model can be used with confidence. The empirical application to stock markets also indicates that a non normal error distribution tends to improve the volatility forecast of returns. Conclusion : The volatility forecast estimates of the best fitted model can be reliably used for volatility forecasting. Moreover, the empirical studies demonstrate that a skewed error distribution outperforms other error distributions in terms of out-of-sample volatility forecasting.

Performance of GARCH models in forecasting stock market volatility

Journal of Forecasting, 1999

We investigate the asymmetry between positive and negative returns in their effect on conditional variance of the stock market index and incorporate the characteristics to form an out-of-sample volatility forecast. Contrary to prior evidence, however, the results in this paper suggest that no asymmetric GARCH model is superior to basic GARCH(1,1) model. It is our prior knowledge that, for equity returns, it is unlikely that positive and negative shocks have the same impact on the volatility. In order to reflect this intuition, we implement three diagnostic tests for volatility models: the Sign Bias Test, the Negative Size Bias Test, and the Positive Size Bias Test and the tests against the alternatives of QGARCH and GJR-GARCH. The asymmetry test results indicate that the sign and the size of the unexpected return shock do not influence current volatility differently which contradicts our presumption that there are asymmetric effects in the stock market volatility. This result is in line with various diagnostic tests which are designed to determine whether the GARCH(1,1) volatility estimates adequately represent the data. The diagnostic tests in section 2 indicate that the GARCH(1,1) model for weekly KOSPI returns is robust to the misspecification test. We also investigate two representative asymmetric GARCH models, QGARCH and GJR-GARCH model, for our out-of-sample forecasting performance. The out-of-sample forecasting ability test reveals that no single model is clearly outperforming. It is seen that the GJR-GARCH and QGARCH model give mixed results in forecasting ability on all four criteria across all forecast horizons considered. Also, the predictive accuracy test of Diebold and Mariano based on both absolute and squared prediction errors suggest that the forecasts from the linear and asymmetric GARCH models need not be significantly different from each other. 1980~2009년의 주간 KOSPI 수익률 시계열의 비대칭 GARCH 모형(Asymmetric GARCH Model)을 이용한 실시간 변동성 예측과 GARCH(1,1) 모형의 실시간 변동성 예측력을 비교하였다. 먼저 2장에서는 GARCH(1,1) 벤치마크 모형을 추정한 후 추정오차가 모형 추정의 전제 조건들을 만족시키는지를 검정하고, 추정오차가 정규분포와 ′ -분포를 취하 는 경우를 가정한 분석을 통해 ′ -분포가 표본데이터에 적합함을 확인하였 다. 3장에서는 주식시장에서 관찰되는 레버리지 효과 -즉 주식시장에 대한 음의 충격 (negative shock) 혹은 부정적인 정보(bad news)가 주식시장의 변동성에 미치는 효과 와 같은 크기의 양의 충격(positive shock) 혹은 긍정적인 정보(good news)가 주식시 장의 변동성에 미치는 효과 -를 반영한 비대칭 GARCH 모형을 이용하였다. 비대칭 GARCH 모형으로 EGARCH, GJR-GARCH, PGARCH 모형을 추정하고, 추정오차를 분석함으로써 어떠한 비대칭 GARCH 모형이 표본데이터에 가장 적합한지 검토하였다. 비대칭 GARCH 효과가 존재하는지에 대한 Sign Bias 검정, Negative Size Bias 검정, Positive Size Bias 검정과 Hagerud(1997) 검정을 통해 표본데이터에 존재하는 비대칭 GARCH 효과의 존재를 확인하였다. 4장에서는 QGARCH 모형과 GJR-GARCH 모형 의 실시간 예측력을 벤치마크모형인 GARCH(1,1)의 실시간 예측력과 비교함으로써 표 본데이터에 존재하는 비대칭 GARCH 효과를 반영한 비대칭 GARCH 모형을 통해 표본 외 예측가능성(Out-of-sample forecasting)을 높일 수 있는지를 검증하였다. 본 연구의 표본데이터를 GARCH(1,1) 모형에 적합(fit)하였을 때, 추정오차가 대부분의 misspecification 검정을 통과하였음을 확인할 수 있었고, GARCH(1,1) 모형과 비대칭 GARCH 모형의 표본외 예측력이 같다는 귀무가설을 통계적으로 기각할 수 없었음을 감안할 때, 우리의 표본기간에 있어서 KOSPI 수익의 분산시계열에는 통계적으로 유의 한 비대칭 GARCH 효과가 존재하지 않으며, 따라서 표본외 예측력에서도 GARCH(1,1) 모형이 비대칭 GARCH 모형과 통계적으로 같음을 확인할 수 있었다.

IJERT-Estimating and Forecasting Stock Market Volatility using GARCH Models: Empirical Evidence from Saudi Arabia

International Journal of Engineering Research and Technology (IJERT), 2015

https://www.ijert.org/estimating-and-forecasting-stock-market-volatility-using-garch-models-empirical-evidence-from-saudi-arabia https://www.ijert.org/research/estimating-and-forecasting-stock-market-volatility-using-garch-models-empirical-evidence-from-saudi-arabia-IJERTV4IS020150.pdf In this paper we used symmetric and asymmetric GARCH models such as GARCH(1,1) ,EGARCH(1,1) and GRJ-GARCH(1,1) models to estimate and forecast volatility of Saudi stock market under various assumptions namely: Normal,Student-t and GED distributions .The study carried out using daily closing prices index over the period of 1 st January 2005 to 31 st December 2012. The common measures of forecast evaluation of the models such as Root Mean Square Errors(RMSE), Mean Absolute Errors (MAE), Mean Absolute Percentage Errors(MAPE) and Theil Inequality Coefficient(TIC) were computed .The empirical results showed that the asymmetric GARCH models with a heavy-tailed error distribution better than the symmetric GARCH model in the estimation the conditional variance equations. Moreover ,we found that the GRJ-GARCH(1,1) model provide the best out-of-sample forecast for Saudi stock market. Finally, the empirical results reveal that conditional variance process is highly persistent and confirm the presence of leverage effect in returns of Saudi stock market.

A Range-Based GARCH Model for Forecasting Volatility

A new variant of the ARCH class of models for forecasting the conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the “realized volatility” model which requires a large amount of intra-daily data that remain relatively costly and are not readily available. The estimates of the GARCH-PARK-R model are derived using the Quasi-Maximum Likelihood Estimation (QMLE). The results suggest that the GARCHPARK- R model is a good middle ground between intra-daily models, such as the realized volatility, and inter-daily models, such as the ARCH class. The forecasting performance of the models is evaluated using the daily Philippine Peso-U.S. Dollar exchange rate from January 1997 to December 2003.

Forecasting volatility in Asian and European Stock Markets with asymmetric GARCH models

2006

II 1. INTRODUCTION 2. ASYMMETRIC GARCH MODELS: VS-GARCH, GJR-GARCH AND Q-GARCH 2.1 The GJR-GARCH model 2.2 The VS-GARCH model 2.3 The Q-GARCH model 2.4 Forecast errors 3. FORECASTING EVALUATION METHODS FOR ASYMMETRIC GARCH MODELS 3.1 Classical evaluation criteria 3.2 Forecast combination 4. EMPIRICAL RESULTS 4.1 Results from classical evaluation criteria 4.2 Results from forecast combination 5.