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Qualitative threshold ARCH models. (English) Zbl 0792.62103
The paper deals with the tradeoff between the flexibility of the conditional variance specification in terms of a given past value and the number of lags. A class of dynamic models is considered (QTARCH models) in which both the conditional mean and the conditional variance are symmetrically treated in order to discuss the possible cross-effects or misspecifications.
The consideration of piecewise constant functions allows the authors to analyze their stochastic properties, discussing the consequences of certain specification errors. The expressions and the asymptotic properties of the pseudo-maximum likelihood estimators of the parameters are also given. These interesting results are also illustrated by the investigation of the Paris stock index in the period January 1986 – April 1990.
Reviewer: R.Pérez (Oviedo)

##### MSC:
 62P20 Applications of statistics to economics 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 91B84 Economic time series analysis
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