PERIODIC COVARIANCE STATIONARITY OF MULTIVARIATE PERIODIC AUTOREGRESSIVE MOVING AVERAGE PROCESSES

1990-05-01
ULA, TA
Periodic (covariance) Stationarity conditions for multivariate periodic autoregressive moving average (PARMA) processes are investigated. It follows from a previous work that a necessary and sufficient condition for the periodic Stationarity of a multivariate periodic process is the (covariance) Stationarity of the “lumped” vector process which contains the periodic vectors as its elements. It is shown that for univariate and multivariate PARMA processes, even with periodically varying orders, the lumped process is a multivariate autoregressive moving average ARMA process, the Stationarity conditions of which are readily available. Periodic Stationarity conditions for the multivariate PARMA (1, 1) process are explicitly obtained, which apply for all PARMA (1, q) processes. It is shown that the periodic Stationarity of a periodic process always implies the Stationarity of the aggregated process, the sum of the periodic vectors. The reverse is yet to be proved or disproved. However, it is shown to be true for PAR(1) and PARMA (1, 1) processes.
WATER RESOURCES RESEARCH

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Citation Formats
T. ULA, “PERIODIC COVARIANCE STATIONARITY OF MULTIVARIATE PERIODIC AUTOREGRESSIVE MOVING AVERAGE PROCESSES,” WATER RESOURCES RESEARCH, pp. 855–861, 1990, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64242.