Random coefficient minification processes

A common way to model nonnegative time series is to apply a log transformation and then use classical ARMA techniques. We demonstrate using Canadian Fire Weather Index (FWI) data that simulating from such models can lead to unrealistic data scenarios. Minification models provide another approach to nonnegative time series, but they can be too restrictive. We propose a random coefficient version of these processes, whose stationarity properties we study in this paper. This model has more flexibility than the fixed coefficient version of the process, and we demonstrate that simulated data from this model can be more realistic, and is so for the FWI series.