Wavelet Analysis of Economic Time Series

Abstract: Economic theory commonly distinguishes between different time horizons such as the short run and the long run. Models with many time horizons are easily studied in the frequency domain, because the various time horizons are associated with a particular frequency or band of frequencies. This dissertation studies wavelet methods to analyze time series. Wavelet transforms combine time and frequency resolution, which is an important property of the transform, implying that the wavelet transform can decompose time series that contain non-recurring events, such as regime changes and outliers, into frequency components without misrepresentation. Chapter 2 of the dissertation introduces a new estimator for cointegrated panel data models. The estimator uses first-differenced data to avoid spurious regressions, and the properties of the wavelet domain to identify different time horizons in the data and to estimate a separate model for each. Simulations show that the proposed estimator is better than common cointegration estimators. Chapter 3 focuses on whether long run money growth contains information about future headline inflation. The analysis shows that money and inflation are related one-to-one in the long run and that there is approximately a two year lag between an increase in the money stock and inflation. Chapter 4 introduces a new estimate of core inflation. Inflation is a monetary phenomenon in the long run, but not in the short run. Core inflation is a short run estimate of the monetary inflation rate. Existing estimates of core inflation often fail to account for relative price changes when they estimate core inflation and are therefore likely to be poor estimates of monetary inflation. The proposed estimate of monetary inflation accounts for relative price changes and uses a wavelet based signal extraction algorithm to estimate the monetary inflation rate. Chapter 5, co-authored with Thomas Elger, studies freight transportation activity in Sweden and relates it to key economic variables. It shows that there is a strong correlation between short run and medium run fluctuations in the economy and freight transportation. There is also a relationship in the long run, but it is not as strong as for the shorter horizons. The Technical Appendix at the end of the dissertation discusses the frequency domain, Fourier transforms, and wavelet transforms in general.