COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1219

Descriptive Econometrics for Nonstationary Time Series
with Empirical Illustrations

Peter C. B. Phillips

June 1999

Recent work by the author on methods of spatial density analysis for time series data with stochastic trends is reviewed and extended. The methods are illustrated in some empirical applications and simulations. The empirical applications include macroeconomic data on inflation, financial data on exchange rates and political opinion poll data. It is shown how the methods can be used to measure empirical hazard rates for inflation and deflation. Empirical estimates based on historical US data over the last 60 years indicate that the predominant inflation risks are at low levels (2–6%) and low two-digit levels (10–12%), and that there is also a significant risk of deflation around the –1% level.

Keywords and Phrases: descriptive statistics, hazard rate, kernel estimate, soujourn time, spatial density, spatial moments, unit root nonstationarity