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

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 of the conventional time-domain and frequency-domain methods in catering for truly evolving phenomena leads us to focus on wavelet analysis. An innovative account of the classical dyadic wavelets analysis is presented in Chapter 5. Chapter 7 suggests how to pursue a non-dyadic wavelet analysis when data structures do not fall neatly into dyadic time and frequency bands; and a new theoretical framework is presented. Interspersed through the thesis are three chapters of empirical applications, which assist in clarifying the theoretical aspects. The first of these, which is Chapter 4, is a comparative analysis of economic cycles experienced by six OECD countries, based on a stylised model the parameters of which are estimated by processing the data in novel ways. In Chapter 6, wavelet shrinkage techniques are applied to the series of UK real GDP. The number and the dates of the structural breaks are identified. In Chapter 8, wavelet analysis is used to help in determining whether or not the volatility of the growth rate of US output has changed since the 1960's, and to attribute a precise date to any marked change.