This chapter deals with the problem of estimating the parameters of an ARIMA model based on the observed time series Y1, Y2,…, Yn. We assume that a model has already been specified; that is, we have specified values for p, d, and q using the methods of Chapter 6. With regard to nonstationarity, since the dth difference of the observed series is assumed to be a stationary ARMA(p,q) process, we need only concern ourselves with the problem of estimating the parameters in such stationary models. In practice, then we treat the dth difference of the original time series as the time series from which we estimate the parameters of the complete model. For simplicity, we shall let Y1, Y2,…, Yn denote our observed stationary process even though it may be an appropriate difference of the original series. We first discuss the method-of-moments estimators, then the least squares estimators, and finally full maximum likelihood estimators.
KeywordsMaximum Likelihood Estimate Autoregressive Model ARIMA Model Bootstrap Confidence Interval Simulated Series
Unable to display preview. Download preview PDF.