Periodic ARMA models: Application to particulate matter concentrations

We propose the use of multivariate version of Whittle's methodology to estimate periodic autoregressive moving average models. In the literature, this estimator has been widely used to deal with large data sets, since, in this context, its performance is similar to the Gaussian maximum likelihood estimator and the estimates are obtained much faster. Here, the usefulness of Whittle estimator is illustrated by a Monte Carlo simulation and by fitting the periodic autoregressive moving average model to daily mean concentrations of particulate matter observed in Cariacica, Brazil. The results confirm the potentiality of Whittle estimator when applied to periodic time series.