Relationship Between Missing Data Likelihoods and Complete Data Restricted Likelihoods for Regression Time Series Models: An Application to Total Ozone Data

Abstract

SUMMARY The relationship is shown between the likelihood of autoregressive moving average (ARMA) models, or the restricted likelihood of a regression model with ARMA errors with possibly non-consecutive data, and the restricted likelihood when the missing values are filled in with Os and regression terms are added to account for the missing values. The latter method is also useful to model additive outliers in a time series setting. This relationship is then used to fit the models with standard computer packages and the results are applied to the analysis of total ozone time series data that involve missing values.