Evaluating the performance of GARCH models using White´s Reality Check (original) (raw)
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Evaluating the Forecasting Performance of GARCH Models Using White’s Reality Check
Brazilian Review of Econometrics, 2005
The important issue of forecasting volatilities brings the difficult task of back-testing the forecasting performance. As volatility cannot be observed directly, one has to use an observable proxy for volatility or a utility function to assess the prediction quality. This kind of procedure can easily lead to poor assessment. The goal of this paper is to compare different volatility models and different performance measures using White's Reality Check. The Reality Check consists of a non-parametric test that checks if any of a number of ...
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.
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.
Comparing the forecasting performance of different GARCH models in international markets
2017
This paper concentrates on the forecasting performance of different GARCH models in five different stock indexes: Eurostoxx50, Nikkei, FTSE100, S&P500, and CAC. The models which are used to forecast volatility are GARCH(1,1), EGARCH, APARCH, CGARCH, and GJR. This paper will perform an in-sample estimation of these GARCH models and then will compare their out of sample forecasting performance. In addition to that we will perform Diebold-Mariano tests to evaluate the predictive accuracy of the models
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.
2017
This paper compares the forecasting performance of univariate (EGARCH) and multivariate GARCH models for the volatilities of stock market index returns of Japan, India, Indonesia and Pakistan each paired with the US stock market. We also investigate the role of Global Financial Crisis (GFC) of 2007-2009 in affecting forecasting performance. We investigate whether incorporation of the linkage with the US stock market in a multivariate GARCH framework helps in improving the volatility forecasts of Asian stock markets. The daily stock returns from July 3, 1997 to November 12, 2012 are employed. Forecasts are evaluated using three measures namely, R (coefficient of determination), Mean Absolute Percentage Error (MAPE) and Median Absolute Percentage Error (MdAPE). The results show that correlation with the US helps in improving the accuracy of volatility forecast of Asian stock markets i.e. performance of multivariate GARCH is found to be better than the EGARCH for all the countries cons...
Empirical performance of GARCH, GARCH-M, GJR-GARCH and log-GARCH models for returns volatility
Journal of Physics: Conference Series, 2019
Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter ...