A Jackknife Correction to a Test for Cointegration Rank

Marcus Chambers

doi:10.3390/econometrics3020355

Abstract

This paper investigates the performance of a jackknife correction to a test for cointegration rank in a vector autoregressive system. The limiting distributions of the jackknife-corrected statistics are derived and the critical values of these distributions are tabulated. Based on these critical values the finite sample size and power properties of the jackknife-corrected tests are compared with the usual rank test statistic as well as statistics involving a small sample correction and a Bartlett correction, in addition to a bootstrap method. The simulations reveal that all of the corrected tests can provide finite sample size improvements, while maintaining power, although the bootstrap procedure is the most robust across the simulation designs considered.

Highlights

The concept of cointegration has assumed a prominent role in the analysis of economic and financial time series since the pioneering work of Engle and Granger [1], and tests for the cointegration rank of a vector of time series have become an essential part of the applied econometrician’s toolkit
The most popular test for cointegration rank is the trace statistic proposed by Johansen [2,3] which exploits the reduced rank regression techniques of Anderson [4] in the context of a vector autoregressive (VAR)
The limiting distribution of the test statistic can be expressed as a functional of a vector Brownian motion process, the dimension of which depends upon the difference between the number of variables under consideration and the cointegration rank under the null hypothesis

Summary

Introduction

The concept of cointegration has assumed a prominent role in the analysis of economic and financial time series since the pioneering work of Engle and Granger [1], and tests for the cointegration rank of a vector of time series have become an essential part of the applied econometrician’s toolkit. The most popular test for cointegration rank is the trace statistic proposed by Johansen [2,3] which exploits the reduced rank regression techniques of Anderson [4] in the context of a vector autoregressive (VAR). The limiting distribution of the test statistic can be expressed as a functional of a vector Brownian motion process, the dimension of which depends upon the difference between the number of variables under consideration and the cointegration rank under the null hypothesis. Toda [8,9] found that the performance of the tests is dependent on the value of the stationary roots of the process, and that a sample of 100 observations is insufficient to detect the true cointegrating rank when the stationary root is close to one (0.8 or above).

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