Empirical process of the squared residuals of an arch\n\t\t\t sequence

Lajos H. Horvath · Gilles Teyssière

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Financial Risk and Volatility Modeling Advanced Statistical Process Monitoring Time Series Analysis and Forecasting

Abstract

We derive the asymptotic distribution of the sequential empirical\nprocess of the squared residuals of an ARCH(p) sequence. Unlike the\nresiduals of an ARMA process, these residuals do not behave in this context\nlike asymptotically independent random variables, and the asymptotic\ndistribution involves a term depending on the parameters of the model. We show\nthat in certain applications, including the detection of changes in the\ndistribution of the unobservable innovations, our result leads to\nasymptotically distribution free statistics.

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References

1997Limit theorems in change-point analysis 1999ARCH Models and Financial Applications 1997ARCH Models and Financial Applications 1985Testing and estimating change-points in time series 1994ON THE SQUARED RESIDUAL AUTOCORRELATIONS IN NON‐LINEAR TIME SERIES WITH CONDITIONAL HETEROSKEDASTICITY 1998The sample autocorrelations of heavy-tailed processes with applications to ARCH 2002Evaluating GARCH models 1999FOURTH MOMENT STRUCTURE OF THE GARCH( p , q ) PROCESS

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