Based on simple time series plots and periodic sample autocorrelations, we document that monthly river flow data display long memory, in addition to pronounced seasonality. In fact, it appears that the long memory characteristics vary with the season. To describe these two properties jointly, we propose a seasonal periodic long memory model and fit it to the well-known Fraser river data (to be obtained from Statlib at We provide a statistical analysis and provide impulse response functions to show that shocks in certain months of the year have a longer lasting impact than those in other months.

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Keywords Long Memory, PARFIMA, Periodic model, SPARFIMA, Seasonal difference
Persistent URL
Series Econometric Institute Research Papers
Ooms, M, & Franses, Ph.H.B.F. (1998). A seasonal periodic long memory model for monthly river flows (No. EI 9842). Econometric Institute Research Papers. Retrieved from