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Spectral Structures in Econometrics: Modern Techniques in Wavelet Analysis and Band Limited Estimation

2007

This thesis presents a number of innovative techniques that can be used in the analysis of econometric data sequences in which the underlying components can be identified by their spectral signatures. To present these techniques intelligibly requires the preparatory expositions of Fourier analysis and of the theory of linear filtering that are presented in Chapters 2 and 3. Amongst the techniques for extracting components from short non stationary sequences that are described in Chapter 3 is a variant of the Hodrick--Prescott filter with a smoothing parameter that varies locally. This enables us to extract from the data trends that incorporate a number of structural breaks. The inadequacy o…