A COMPARISON OF CONFIDENCE INTERVALS IN STATE SPACE MODELS

This thesis develops general procedures for constructing confidence intervals (CIs) of the error disturbance parameters (standard deviations) and transformations of the error disturbance parameters in time-invariant state space models (ssm). With only a set of observations, estimating individual error disturbance parameters accurately in the presence of other unknown parameters in ssm is a very challenging problem. We attempted to construct four different types of confidence intervals, Wald, likelihood ratio, score, and higher-order asymptotic intervals for both the simple local level model and the general time-invariant state space models (ssm). We show that for a simple local level model, both the likelihood ratio interval and the higher-order asymptotic interval have superior performance with underage, coverage, and overage accurate to 1% of the target values. For the general time-invariant ssm, we focus on constructing CIs for the correlation coefficient ρ of the standard deviations of the accelerations in a two-dimensional object tracking example. Results show that the likelihood ratio method can achieve underage, coverage, and overage accurate to 1% of the target values, whereas the Wald method has far inferior performance. Weighing the theoretical and computational complexities of all four methods, we consider the likelihood ratio method as the most practical method for constructing confidence intervals (CIs) of the error disturbance parameters in time-invariant ssm