Modelling multiple time series with missing observations

Abstract

This thesis introduces an approach to the state space modelling of time series that may possess missing observations. The procedure starts by estimating the autocovariance sequence using an idea proposed by Parzen(1963) and Stoffer(1986). Successive Hankel matrices are obtained via Autoregressive approximations. The rank of the Hankel matrix is determined by a singular value decomposition in conjunction with an appropriate model selection criterion . An in tern ally balanced state space realisation of the selected Hankel matrix provides initial estimate for maximum likelihood estimation. Finally, theoretical evaluation of the Fisher information matrix with missing observations is considered. The methodology is illustrated by applying the implied algorithm to real data. We consider modelling the white blood cell counts of a patient who has Leukaemia. Our modelling objective is to be able to describe the dynamic behaviour of the white blood cell counts.