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On a threshold autoregression with conditional heteroscedastic variances. (English) Zbl 0921.62113
This paper considers time series models with a piecewise linear conditional mean and a piecewise linear conditional variance function. These models combine elements of the traditional threshold autoregressive models capable of modeling time series with jumps and limit cycles, and the ARCH/GARCH models used to represent conditional heteroscedastic variances. These models appear well-suited for modeling financial time series as is illustrated by an analysis of daily returns of the Hong Kong Seng Index. The authors establish conditions for stationarity and ergodicity. They also derive maximum likelihood estimators of the underlying parameters and study their asymptotic properties. Residuals of the fitted model are used as a check on the adequacy of the model.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G70 Statistical methods; risk measures
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