A UNIFIED APPROACH TO THE STUDY OF SUMS, PRODUCTS, TIME‐AGGREGATION AND OTHER FUNCTIONS OF ARMA PROCESSES

E. M. R. A. Engel

Journal of Time Series Analysis, 1984, vol. 5, issue 3, 159-171

Abstract: Abstract. Conditions under which sums, products and time‐aggregation of ARMA processes follow ARMA models are derived from a single theorem. This characterizes these processes in terms of difference equations satisfied by their autocovariance function. From this we obtain necessary and sufficient conditions for a function of a Gaussian ARMA process and the product of two possibly dependent Gaussian ARMA processes to be ARMA. We show that the sum and product of two ARMA processes related by a Box and Jenkins transfer function model belong to the ARMA family.

Date: 1984
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