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A simple integer-valued bilinear time series model. (English) Zbl 1096.62082

Summary: We extend the integer-valued model class to give a nonnegative integer-valued bilinear process, denoted by INBL\((p,q,m,n)\), similar to the real-valued bilinear model. We demonstrate the existence of this strictly stationary process and give an existence condition for it. The estimation problem is discussed in the context of a particular simple case. The method of moments is applied and the asymptotic joint distribution of the estimators is given: it turns out to be a normal distribution. We present numerical examples and applications of the model to real time series data on Meningitis and Escherichia coli infections.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes
62E20 Asymptotic distribution theory in statistics
62F10 Point estimation

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