Innovations algorithm for periodically stationary time series

Periodic ARMA, or PARMA, time series are used to model periodically stationary time series. In this paper we develop the innovations algorithm for periodically stationary processes. We then show how the algorithm can be used to obtain parameter estimates for the PARMA model. These estimates are proven to be weakly consistent for PARMA processes whose underlying noise sequence has either finite or infinite fourth moment. Since many time series from the fields of economics and hydrology exhibit heavy tails, the results regarding the infinite fourth moment case are of particular interest.