A periodically integrated autoregressive process for a time series which is observed S times per year assumes the presence of S - 1 cointegration relations between the annual series containing the seasonal observations, with the additional feature that these relations are different across the seasons. This means that there is a single unit root in the vector autoregression for these annual series. In this paper it is shown that temporally aggregating such a process does not affect the presence of this unit root, i.e. the aggregated series is also periodically integrated.

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Keywords autoregression models, cointegration, time series
Persistent URL dx.doi.org/10.1016/0167-7152(95)00225-1, hdl.handle.net/1765/2063
Journal Statistics & Probability Letters
Citation
Franses, Ph.H.B.F, & Boswijk, H.P. (1996). Temporal aggregation in a periodically integrated autoregressive process. Statistics & Probability Letters, 30(3), 235–240. doi:10.1016/0167-7152(95)00225-1