| An attraction of fractional processes is that they allow more flexibility in the dynamic responses of economic variables to shocks than is permitted under the unit root model. In Particular, these favorable properties of flexibility and slow convergence to equilibrium levels render fractional integration an attractive model of time series behavior, a model that accommodates unit root type persistence as well as long range dependence and mean reversion. Several methods have been proposed to estimate the fractional integration parameter d. Sowell (1990b) proposes a maximum likelihood method to estimate d and the ARMA (p, q) parameters jointly. In this dissertation we investigate the presence of fractional dynamics in several important macroeconomic and financial time series.; The purpose is to apply the new ARFIMA methodology to distinguish between different models of long-run behavior i.e. nesting the difference stationary and trend stationary models. In particular, we analyze the long-term dynamic behavior of discreetly observed data at monthly and quarterly frequencies for the G-7 countries spanning the period from 1961 through 2000. First, in this dissertation fractional time series models are estimated using a relatively new maximum likelihood procedure (Li and McLeod, 1986; and Sowell, 1990b). Second, we provide some international evidence on persistence using post war data for the G-7 countries. Finally, the data set includes two output measures, two components of the gross domestic product (GDP), two measures of inflation, two measures of interest rates, a broad money stock measure and the real effective exchange rate.; Our results often deviated from the stylized facts reported in the literature. For example, fractional behavior in per capita GDP was not unique to the United States as is often reported. Another example that deviates from the stylized facts in the literature is that seasonally adjusting a series did not contribute to measurable differences. There was no evidence of persistence in long-term interest rates for all countries, whereas persistence was statistically significant in short-term rates for Germany, the UK and the US. The ARFIMA model is established as an appropriate representation of the stochastic behavior of French, German, Italian, UK and US money stock. |
