Seasonal Time Series Models with Periodic Variances

This paper studies two types of seasonal time series models with periodic variances. Covariance structures of the noise component in the models are discussed. For parameters in the regression component, the performance of the least squares estimates relative to the best linear unbiased estimates is investigated, and some lower bounds for the eecient coeecient deened by the covariance matrices of parameter estimates are given. Maximum likelihood estimation for parameters in the models is discussed when some observations are missing. The seasonal time series models are applied to a global-average total ozone data set for long-term trend assessment, where a modiied Schwartz's Bayesian Criterion is used for model selection.