Nonlinear time series analysis using a Monte-Carlo smoother

Applications of state space models in nonlinear and/or non-Gaussian settings are very much a reality. The Kalman filter and the Kalman smoother offer optimal solutions in the linear Gaussian setting. However, in the nonlinear setting, while particle filtering theory and practice can be considered well established, particle smoothing is yet to be thoroughly explored.;Using a simple linear Gaussian model, comparisons are conducted to ensure that Monte Carlo filtering and smoothing techniques perform in a manner consistent with the Kalman filter and Kalman smoother in the linear-Gaussian setting and also to determine how the filter and smoother differ from one another under various conditions. Possible techniques are explored to determine how to select an appropriate lag size when conducting fixed-lag Monte Carlo smoothing as a means to approximate the fixed-interval smoother. As well, attempts to determine appropriate particle set sizes for the implementation of the SIR filter and the Monte Carlo smoother are also made using the Kalman results as a comparison.;Kitagawa's fixed-lag Monte Carlo smoother is applied to a nonlinear non-Gaussian state space model using techniques suggested for the determination of an appropriate lag size by consideration of the linear Gaussian model. The state state model considered is discussed by Dowd (2006) and consists of process oriented dynamic ecosystem models combined with marine observations.;The focus of this thesis is on Monte Carlo methods for nonlinear non-Gaussian filtering and smoothing discussed by Kitagawa (1996). These methods as well as their algorithms are discussed in detail. The exact solutions for the linear Gaussian case provided by the Kalman filter and fixed-interval Kalman smoother are also discussed and their algorithms are outlined and applied.