A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model

This paper explores seasonal and long-memory time series properties by using the fractional ARIMA model when the data have one and two seasonal periods and short-memory components. The stationarity and invertibility parameter conditions are established for the model studied. To estimate the seasonal fractional long-memory parameters, a semiparametric estimation method is proposed. The asymptotic properties of the estimator are established and the accuracy of the method is investigated through Monte Carlo experiments. The good performance of the estimator indicates that it can be an alternative procedure to estimate long-memory time series data with two seasonal periods. Series of PM10 concentrations and electricity hourly demand are considered as examples of applications of the proposed estimation method.