Inspecting a seasonal ARIMA model with a random period

This work proposes a class of seasonal autoregressive integrated moving average models whose period is an independent and identically distributed random process valued in a finite set. The causality, invertibility, and autocovariance shape of the model are first revealed. Then, the estimation of the parameters which are the model coefficients, the innovation variance, the probability distribution of the period, and the (unobserved) sample-path of the period, is carried out using the expectation-maximization algorithm. In particular, a procedure for random elimination of seasonality is proposed. An application of the methodology to the annual Wolfer sunspot numbers is provided.