Seasonal and Periodic Long Memory Models in the In�ation Rates

This paper considers the application of long memory processes to describe inflation with seasonal behaviour. We use three different long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the periodic ARFIMA (PARFIMA) model. These models are used to describe the inflation rates of four different countries, USA, Canada, Tunisia, and South Africa. The analysis is carried out using the Sowell's (1992) maximum likelihood techniques for estimating ARFIMA model and using the approximate maximum likelihood method for the estimation of the PARFIMA process. We implement a new procedure to obtain the maximum likelihood estimates of the ARFISMA model, in which dummies variables on additive outliers are included. The advantage of this parametric estimation method is that all parameters are estimated simultaneously in the time domain. For all countries, we find that estimates of differencing parameters are significantly different from zero. This is evidence in favour of long memory and suggests that persistence is a common feature for inflation series. Note that neglecting the existence of additive outliers may possibly biased estimates of the seasonal and periodic long memory models.