Estimation of Time Series Models. Part I. Yet another Algorithm for the Exact Likelihood of ARMA (Autoregressive-Moving Average) Models

摘要

This paper presents a method for calculating the likelihood function of autoregressive-moving average (ARMA) models for time series data. Model estimation requires maximization of the likelihood, and to assist in this, a method for calculating derivatives of the function is also presented. The computational efficiency is competitive with that of other algorithms for this purpose. Extensions which allow for seasonal models, missing data, and the estimation of a data transformation are also described. (Author)