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On the memory of products of long range dependent time series. (English) Zbl 1396.91346

Summary: This paper derives the memory of the product series \(x_ty_t\), where \(x_t\) and \(y_t\) are stationary long memory time series of orders \(d_x\) and \(d_y\), respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of products of series with non-zero means is determined by the maximal memory of the factor series, whereas the memory is reduced if the series are mean zero.

MSC:

91B38 Production theory, theory of the firm
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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