State space models and estimation of missing observations in time series
Biwott, Daniel Kiprotich
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In this project we have considered a non-linear time series model, which encompasses several standard non-linear models for time series as special cases. It also offers two methods for estimating missing observations, one using prediction and fixed point smoothing algorithm and the other using optimal estimating equation theory. Recursive estimation of missing observations in an Autoregressive Conditionally Heteroscedastic (ARCH) model and the estimation of missing observations in a linear time series model are shown to be special cases. For the case of prediction and fixed point smoothing algorithm, we have generalised the formula developed by Abraham and Thavaneswaran (1991) for estimating missing observations to a case when there are more than two missing observations. Simulation studies have been carried out on AR 91) data to illustrate the application of the formula.