A variety of topics on the statistical analysis of time series are addressed in this thesis. The main emphasis is on the state space methodology and, in particular, on structural time series (STS) models. There are now many applications of STS models in the literature and they have proved to be very successful. The keywords of this thesis vary from - Kalman filter, smoothing and diagnostic checking - to - time-varying cubic splines and intra-daily effects -. Five separate studies are carried out for this research project and they are reflected in the chapters 2 to 6. All studies concern time series models which are placed in the state space form (SSF) so that the Kalman filter (KF) can be applied for estimation. The SSF and the KF play a central role in time series analysis that can be compared with the important role of the regression model and the method of least squares estimation in econometrics. Chapter 2 gives an overview of the latest developments in the state space methodology including diffuse likelihood evaluation, stable calculations, etc. Smoothing algorithms evaluate the full sample estimates of unobserved components in time series models. New smoothing algorithms are developed for the state and the disturbance vector of the SSF which are computationally efficient and outperform existing methods. Chapter 3 discusses the existing and the new smoothing algorithms with an emphasis on theory, algorithms and practical implications. The new smoothing results pave the way to use auxiliary residuals, that is full sample estimates of the disturbances, for diagnostic checking of unobserved components time series models. Chapter 4 develops test statistics for auxiliary residuals and it presents applications showing how they can be used to detect and distinguish between outliers and structural change. A cubic spline is a polynomial function of order three which is regularly used for interpolation and curve-fitting. It has also been applied to piecewise regressions, density approximations, etc. Chapter 5 develops the cubic spline further by allowing it to vary over time and by introducing it into time series models. These timevarying cubic splines are an efficient way of handling slowly changing periodic movements in time series. This method for modelling a changing periodic pattern is applied in a structural time series model used to forecast hourly electricity load demand, with the periodic movements being intradaily or intra-weekly. The full model contains other components, including a temperature response which is also modelled using cubic splines. A statistical computer package (SHELF) is developed to produce, at any time, hourly load forecasts three days ahead.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:543121 |
| Date | January 1992 |
| Creators | Koopman, Siem Jan |
| Publisher | London School of Economics and Political Science (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.lse.ac.uk/74/ |
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