Volatility Modeling and Value-at-Risk (VaR) Forecasting of Emerging Stock Markets in the Presence of Long Memory, Asymmetry, and Skewed Heavy Tails

Abstract

In this article, we elaborate some empirical stylized facts of eight emerging stock markets for estimating one-day- and one-week-ahead Value-at-Risk (VaR) in the case of both short- and long-trading positions. We model the emerging equity market returns via APARCH, FIGARCH, and FIAPARCH models under Student-t and skewed Student-t innovations. The FIAPARCH models under skewed Student-t distribution provide the best fit for all the equity market returns. Furthermore, we model the daily and one-week-ahead market risks with the conditional volatilities generated from the FIAPARCH models and document that the skewed Student-t distribution yields the best results in predicting one-day-ahead VaR forecasts for all the stock markets. The results also reveal that the prediction power of the models deteriorate for longer forecasting horizons.

KEY WORDS:

• emerging stock markets
• GARCH models
• Value-at-Risk
• long memory
• Kupiec test
• Dynamic Quantile test

Notes

^1. The stock markets are BOVESPA, RTSI, SENSEX, SHANGHAI, IPC, JAKARTA, KOSPI and BIST composite indices for Brazil, Russia, India, China, Mexico, Indonesia, South.Korea, and Turkey, respectively.

^2. For mathematical and technical details, see Ng and Perron (2001).

^3. Since the GPH test is very sensitive to the choice of bandwidth selection, we estimate the test with diverse bandwidths: m = T^0.5, m = T^0.6, m = T^0.8.

^4. We investigate the combinations of p = 1, 2, 3… and q = 1, 2, 3 … for all of the models. However, according to the information criteria (SIC) and log likelihood values, the models with lags, p = 1 and q = 1 outperform those with higher lag orders.

^5. As indicated in section 3.2, we use the last 500 observations for the out-of-sample VaR forecasting.

^6. The null hypothesis of the Ljung-Box test imply no serial correlation and the null hypothesis of ARCH LM test is the absence of remaining ARCH effects in a model’s residuals. Hence, in the case of an insignificant value of the tests, the null hypotheses are not rejected.

^7. RBD is the residual based diagnostic test for conditional heteroscedasticity, having the null hypothesis of model adequacy.

^8. For the VaR estimation, we contemplate RiskMetrics and several short memory GARCH-class models. However, these models do not provide better results. The findings are available upon request.

^9. We thank an anonymous referee for his valuable suggestion of longer horizon forecasting.

^10. As backtesting procedures, we also analyze Kupiec and DQ tests for the in-sample analyses. The results point out the superiority of the FIAPARCH model under skewed Student-t errors. To conserve space, we do not display the results here, but they are available upon request.

^11. As an alternative test, we could consider the Christoffersen test (1998). However, the DQ test simultaneously examines whether the proportion of violations are at the expected rate and these violations are not serially correlated. For this reason, we employ the DQ test.

^12. We also estimate two week-ahead (ten trading days) forecasts. Based on Kupiec tests, the number of violations are higher and DQ test results indicate more serially correlated exceptions. To conserve space, we do not present the associated results and they are available upon request.

^13. They report that GARCH-type models are more powerful in forecasting for short horizons.