Portmanteau goodness-of-fit test for asymmetric power GARCH models

Carbon, Michel and Francq, Christian (2010): Portmanteau goodness-of-fit test for asymmetric power GARCH models.

Abstract

The asymptotic distribution of a vector of autocorrelations of squared residuals is derived for a wide class of asymmetric GARCH models. Portmanteau adequacy tests are deduced. %gathered These results are obtained under moment assumptions on the iid process, but fat tails are allowed for the observed process, which is particularly relevant for series of financial returns. A Monte Carlo experiment and an illustration to financial series are also presented.

• Item Type: MPRA Paper
• Language: English
• Keywords: ARCH models; Leverage effect; Portmanteau test; Goodness-of-fit test; Diagnostic checking
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Berkes, L., Horvath, L., Kokoszka, P. (2003). Asymptotics for GARCH squared residual correlations. Econometric Theory, 19, 515–540.

Black, F. (1976). Studies of stock price volatility changes. In Proceedings from the american statistical association, business and economic statistics section (pp. 177– 181).

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.

Bollerslev, T. (2009). Glossary to ARCH (GARCH). In T. Bollerslev, J. Russell, & M. Watson (Eds.), Volatility and time series econometrics: Essays in honor of Robert F. Engle. Oxford, UK: Oxford University Press.

Box, G., Pierce, D. (1970). Distribution of the residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65, 1509-1526.

Brockwell, P., Davis, R. (1991). Time series: Theory and methods (2nd ed.). New York: Springer-Verlag.

Ding, Z., Granger, C., Engle, R. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83-106.

Engle, R. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of the United Kingdom inflation. Econometrica, 50, 987-1007.

Francq, C., Zakoian, J.-M. (2010). Garch models: Structure, statistical inference and financial applications. Chichester, UK: John Wiley.

Glosten, L., Jaganathan, R., Runkle, D. (1993). On the relation between the expected values and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779-1801.

Hamadeh, T., Zakoian, J.-M. (2011). Asymptotic properties of ls and qml estimators for a class of nonlinear GARCH processes. Journal of Statistical Planning and Inference, 141, 488-507.

Li, W. (2004). Diagnostic checks in time series. Boca Raton, Florida: Chapman and Hall.

Li,W., Mak, T. (1994). On the square residual autocorrelations in non-linear time series with conditional heteroscedasticity. Journal of Time Series Analysis, 15, 627-636.

Ling, S., Li, W. (1997). On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association, 92, 1184-1194.

Ljung, G., Box, G. (1978). On the measure of lack of fit in time series models. Biometrika, 65, 297-303.

McLeod, A. (1978). On the distribution of residual autocorrelations in Box-Jenkins method. Journal of the Royal Statistical Society B, 40, 296-302.

Rabemananjara, R., Zakoian, J.-M. (1993). Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics, 8, 31-49.