Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests

Abstract

This article uses Monte Carlo experiments and response surface regressions in a novel way to calculate approximate asymptotic distribution functions for several well-known unit-root and cointegration test statistics. These allow empirical workers to calculate approximate P values for these tests. The results of the article are based on an extensive set of Monte Carlo experiments, which yield finite-sample quantiles for several sample sizes. Based on these, response surface regressions are used to obtain asymptotic quantiles for many different test sizes. Then approximate distribution functions with simple functional forms are estimated from these asymptotic quantiles.

KEY WORDS:

• Approximate P values
• Asymptotic quantiles
• Generalized method of moments
• Monte Carlo
• Response surface