Estimation and Testing for Unit Roots in a Partially Nonstationary Vector Autoregressive Moving Average Model

Sook Fwe Yap · Gregory C. Reinsel

76 citations0/0 files storedJournal of the American Statistical Association

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Monetary Policy and Economic Impact Statistical and numerical algorithms Diverse Scientific and Economic Studies

Abstract

The Gaussian estimation of a partially nonstationary autoregressive model and the related issue of testing for cointegration using the likelihood ratio test procedure have been considered by others. In this article we extend the Gaussian estimation procedure to partially nonstationary autoregressive moving average models and derive the asymptotic properties of the full-rank and reduced-rank Gaussian estimators. Based on these results, the asymptotic distribution of the likelihood ratio statistic for testing the number of unit roots is obtained. A numerical example based on three U.S. interest rate series is used to illustrate the estimation and testing procedures. The finite-sample properties of the estimation and likelihood ratio test procedures are examined through a small simulation study.

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References

1987Co-Integration and Error Correction: Representation, Estimation, and Testing 1988Testing for a Unit Root in Time Series Regression 1988Statistical analysis of cointegration vectors 1990MAXIMUM LIKELIHOOD ESTIMATION AND INFERENCE ON COINTEGRATION — WITH APPLICATIONS TO THE DEMAND FOR MONEY 1991Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models 1984Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order 1990Asymptotic Properties of Residual Based Tests for Cointegration 1988Testing for Common Trends

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