Time series analysis of macroeconometric constructs

This thesis addresses the issue of estimating persistence of economic shocks using time series models. First, it is shown that the log likelihood function for ARIMA models is not strictly quadratic with respect to the persistence estimate. This result explains why the persistence literature has attained conflicting results. In addition, nonparametric estimates of persistence based on the variance ratio are analyzed. It is found that the distribution of the variance ratio statistic depends upon the data generating process of ARIMA models, and that the variance ratio for log U.S. GNP falls within the bounds of simulated variance ratios for models with persistence of zero and persistence greater than one. However, a model adequacy test based on the variance ratio is derived for ARIMA(p, 1, q) model specification; the distribution of the test statistic does not depend upon unknown model parameters. Finally, persistence is analyzed within a multivariate framework. A permanent/transitory components model representation is found for a bivariate vector autoregression for log U.S. GNP and unemployment rates. It is found that there is considerable uncertainty about both the persistence of the permanent component and the implied univariate persistence for even lightly parameterized vector autoregression models.