COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 768 "Mulitple Time Series Regression with Integrated Processes" Peter C.B. Phillips and Steven N. Durlauf September 1985 This paper develops a general asymptotic theory of regression for processes which are
integrated of order one. The theory includes vector autoregressions and multivariate
regressions amongst integrated processes that are driven by innovation sequences which
allow for a wide class of weak dependence and heterogeneity. The models studied cover
cointegrated systems and quite general linear simultaneous equations systems with
contemporaneous regressor-error correlation and serially correlated errors. Problems of
statistical testing in vector autoregressions and multivariate regressions with integrated
processes are also studied. It is shown that the asymptotic theory for conventional tests
involves major departures from classical theory and raises new and important issues of the
presence of nuisance parameters in the limiting distribution theory. |
