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State space models: Univariate representation of a multivariate model, partial interpolation and periodic convergence.

Mavrakakis, Miltiadis C (2008) State space models: Univariate representation of a multivariate model, partial interpolation and periodic convergence. PhD thesis, London School of Economics and Political Science (United Kingdom).

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Abstract

This thesis examines several issues that arise from the state space representation of a multivariate time series model. Original proofs of the algorithms for obtaining interpolated estimates of the state and observation vectors from the Kalman filter smoother (KFS) output are presented, particularly for the formulae for which rigorous proofs do not appear in the existing literature. The notion of partially interpolated estimates is introduced and algorithms for constructing these estimates are established. An existing method for constructing a univariate representation (UR) of a multivariate model is developed further, and applied to a wider class of state space models. The computational benefits of filtering and smoothing with the UR, rather than the original multivariate model, are discussed. The UR KFS recursions produce useful quantities that cannot be obtained from the original multivariate model. The mathematical properties of these quantities are examined and the process of reconstructing the original multivariate KFS output is demonstrated By reversing the UR process, a time-invariant state space form (SSF) is proposed for models with periodic system matrices. This SSF is used to explore the novel concept of periodic convergence of the KFS. Necessary and sufficient conditions for periodic convergence are asserted and proved. The techniques developed are then applied to the problem of missing- value estimation in long multivariate temperature series, which can arise due to gaps in the historical records. These missing values are a hindrance to the study of weather risk and pricing of weather derivatives, as well as the development of climate-dependent models. The proposed model-based techniques are compared to existing methods in the field, as well as an original ad hoc approach. The relative performance of these methods is assessed by their application to data from weather stations in the state of Texas, for daily maximum temperatures from 1950 to 2001.

Item Type: Thesis (PhD)
Uncontrolled Keywords: Statistics
Sets: Collections > ProQuest Etheses
Departments > Statistics
URI: http://etheses.lse.ac.uk/id/eprint/2341

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