On the memory of products of long range dependent time series

•This paper derives the memory of the product of two Gaussian fractionally integrated processes.•Products of fractionally cointegrated series and squared series are also considered.•It is found that the transmission of memory from the factor series to the product series depends critically on the means of the processes.•A Monte Carlo simulation confirms the results.•Implications of the findings for random coefficient models and time series regressions are discussed.

This paper derives the memory of the product series xtyt, where xt and yt are stationary long memory time series of orders dx and dy, 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.