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A conditional least squares approach to bilinear time series estimation. (English) Zbl 0834.62077

Summary: In this paper a conditional least squares (CLS) procedure for estimating bilinear time series models is introduced. This method is applied to a special superdiagonal bilinear model which includes the classical linear autoregressive moving-average model as a particular case and it is proven that the limiting distribution of the CLS estimates is Gaussian and that the law of the iterated logarithm holds.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62M09 Non-Markovian processes: estimation
62E20 Asymptotic distribution theory in statistics
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