Estimating parameters of a multiplicative seasonal ARIMA model using prediction error method algorithm

Estimating the parameters of a model presents only one stage of the time series modeling procedure. This paper describes an effective way of estimating the parameters of the multiplicative seasonal autoregressive integrated moving average (ARIMA) model in a recursive fashion. This ‘on line’ algorithm is, in contrast to the known ‘off line’ algorithms, noniterative and model independent. The method is based on the Gauss-Newton parameter estimator, updating its gradient and Hessian every time instant some new data becomes available.