Forecasting Volatility in China stock market

中图分类号：F832文献标识：A文章编号：1009-4202（2012）02-000-01

AbstractThis paper built three models for forecasting stock market volatility of shanghai composite index and found the GARCH model is better than Random Walk model and ARCH model.

Key Words GARCH, ARCH, Random Walk, volatility

Ⅰ Introduction

There are many literatures forecasting volatility of foreign stock market. Jun Yu(2002) finds the stochastic volatility model provides the best performance for New Zealand stock market. DAVID MCMILLAN, ALAN SPEIGHT and OWAIN APGWILYM(2000) find that the most consistent forecasting performance is provided by moving average and GARCH models. DES NICHOLLS and DAVID TONURI(1995) has examined the behavior of Australian aggregate stock market volatility using the GARCH framework.

Ⅱ Sample Data

The sample is the daily data of Shanghai composite index, from January 1991 to June 2010. The daily return is calculated by , whereis the daily index in day t. According to Merton(1980) and Perry(1982), the monthly volatility is the sum of the squared daily return in that month, that is:, Where is the daily return on day t, andis the number of trading days in month T.

Statistics shows the monthly volatility series is not a normal distribution. And ADF test shows that the series is stationary. The first 16 years (from 1991 to 2006) of data are used to fit the models. As the sample is rolled over, the model is re-estimated and the 1-month ahead forecast is made. Hence, 42 monthly volatilities are forecasted, which are from January 2007 to June 2010.

Ⅲ Candidate models

(1) Random walk

Random walk assumes that, and the best forecast of next month’s volatility is this month’s volatility, that is.

(2)ARCH model

The ARCH(q) model is defined by

, Where~iidN(0,1).

(2.1) Test for stationary to daily return

ADF test and Phillips-perron unit root test also show that daily return has no unit root.

(2.2) Fit an AR model

ACF and PACF of daily return show it has autocorrelation in the first four orders. However, the regression result shows the coefficients of constant and AR(3) is not significant, so the AR model is:

R-squared =0.007987; Durbin-Watson stat= 2.002378

Residual autocorrelation test shows there is no autocorrelation in residual. Thus, the AR model is adequate.

(2.3) ARCH effect test

Correlogram Squared Residual shows there is autocorrelation in the squared residual, that is ARCH effect. The ARCH LM tests for lag 2 to lag 8 are all significant, which means that residual exists high order ARCH effect.

(2.4) Fit ARCH model

The ARCH model is identified basing on several principals: smallest AIC or BIC, coefficients are great than 0 and less than 1, R-squared is greater than 0.

(2.5) Model diagnosis

ARCH LM test to shows that there is no ARCH effect any more. ARCH(7) model is adequate.

(3) GARCH model

Following the same procedures of building ARCH model, an GARCH(2,1) model is identified as follow:

Ⅳ Forecast Evaluation

Root Mean Square Error(RMSE) and the Mean Absolute Error(MAE) are used to evaluate the forecast accuracy: ,.Where is the forecasted monthly volatility, is the actual monthly volatility.

Both RMSE and MAE indicates that the GARCH(2,1) model provides the most accurate forecasts, while the ARCH(7) model ranks second, and random walk model ranks last.

Ⅴ Conclusion

This paper built three models for forecasting stock market volatility of shanghai composite index. After comparing the forecasting performance of the three models, it was found that the GARCH(2,1) model is better than Random Walk model and ARCH model according to RMSE and MAE.

References

[1]JUN YU (2002). Forecasting volatility in the New Zealand stock market, Applied Financial Economics, 12, 193-202.

[2]DAVID MCMILLAN, ALAN SPEIGHT and OWAIN APGWILYM(2000). Forecasting UK stock market volatility, Applied Financial Economics, 10, 435-448.

[3]DES NICHOLLS and DAVID TONURI(1995). Modeling stock market volatility in Australia, Journal of Business Finance & Accounting, 22(3), 377-396.