Portmanteau Goodness-of-Fit Test for Asymmetric Power GARCH Models
DOI:
https://doi.org/10.17713/ajs.v40i1&2.197Abstract
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. 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.References
Berkes, L., Horváth, L., and 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 ASA, 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. R. Russell, and M. Watson (Eds.), Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle. Oxford, UK: Oxford University Press.
Box, G. E. P., and Pierce, D. A. (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. J., and Davis, R. A. (1991). Time Series: Theory and Methods (2nd ed.). New York: Springer-Verlag.
Ding, Z., Granger, C., and Engle, R. F. (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., and Zakoïan, J. (2010). GARCH Models: Structure, Statistical Inference and Financial Applications. Chichester, UK: John Wiley.
Glosten, L. R., Jaganathan, R., and 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., and Zakoïan, J. (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. K. (2004). Diagnostic Checks in Time Series. Boca Raton, Florida: Chapman and Hall.
Li, W. K., and Mak, T. W. (1994). On the square residual autocorrelations in non-linear time series with conditional heteroscedasticity. Journal of Time Series Analysis, 15, 627-636.
Ling, S., and Li, W. K. (1997). On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association, 92, 1184-1194.
Ljung, G. M., and Box, G. E. P. (1978). On the measure of lack of fit in time series models. Biometrika, 65, 297-303.
McLeod, A. I. (1978). On the distribution of residual autocorrelations in Box-Jenkins method. Journal of the Royal Statistical Society B, 40, 296-302.
Rabemananjara, R., and Zakoïan, J. (1993). Threshold ARCH models and asymmetries
in volatility. Journal of Applied Econometrics, 8, 31-49.
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