Testing for Common Trends

Abstract

Abstract Cointegrated multiple time series share at least one common trend. Two tests arc developed for the number of common stochastic trends (i.e. for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic trend. But both casual observation and economic theory suggest that many series might contain the same stochastic trends so that they are cointegrated. Previous researchers have found that U.S. postwar interest rates, taken individually, appear to be integrated of order 1. In addition, the theory of the term structure implies that yields on similar assets of different maturities will be cointcgrated.