Estimating and evaluation economic models via spectral analysis
Spectral density matrices provide a complete summary of the second order dynamics of a multivariate time series. Under the assumption of Gaussianity, then, the spectra together with a description of the mean (or trend) of the time series completely describe the distribution of the data. This dissertation begins by describing some methods for calculating spectra of data. It is well known, however, that such consistent spectral estimates converge only slowly to their asymptotic distributions. I, therefore, provide a survey of existing bootstrap algorithms. These algorithms are designed to provide better approximations to the finite sample distributions of spectra. I then detail two new bootstrap algorithms. The first is explicitly a bootstrap for multivariate spectra. The second algorithm is an omnibus time series bootstrap. The second chapter of the dissertation (based on Diebold, Ohanian and Berkowitz (1995)) describes a general estimation and evaluation framework based on comparing model spectra to data spectra. This type of Simulated Moment Estimation allows the user to calculate the parameter configuration at which all of the second order properties of the model are closest to those properties in the data. The model may then be tested by comparing model generated spectra to bootstrapped confidence bands around data spectra by using the methods of chapter 1. The model can be tested over subsets of frequencies (for example, business cycles). The methods are applied to a model of the well known cycle in U.S. cattle data. The third chapter describes an estimation procedure which is based on the spectrum of residuals. I first note that the deviations from a Euler equation, derived from a rational expectations model, are typically white noise. It is then shown that parameters may be estimated by requiring that the spectrum of these Euler residuals be close to a straight line. The estimation procedure is illustrated with an application to the Monetary Model of exchange rate dynamics.
Berkowitz, Jeremy, "Estimating and evaluation economic models via spectral analysis" (1996). Dissertations available from ProQuest. AAI9627884.