Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2013-11-19
Number: 13-187/III
Author-Name: H. Peter Boswijk
Author-Workplace-Name: University of Amsterdam
Author-Name: Giuseppe Cavaliere
Author-Workplace-Name: University of Bologna, Italy
Author-Name: Anders Rahbek
Author-Workplace-Name: University of Copenhagen, Denmark, and CREATES
Author-Name: A. M. Robert Taylor
Author-Workplace-Name: University of Essex, United Kingdom
Title: Inference on Co-integration Parameters in Heteroskedastic Vector Autoregressions
Abstract: It is well established that the shocks driving many key macro-economic and financial variables display time-varying volatility. In this paper we consider estimation and hypothesis testing on the coefficients of the co-integrating relations and the adjustment coefficients in vector autoregressions driven by both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the conventional results in Johansen (1996) for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold in the presence of heteroskedasticity. As a consequence, standard confidence intervals and tests of hypothesis on these coefficients
are potentially unreliable. Solutions to this inference problem based on Wald tests (using a "sandwich" estimator of the variance matrix) and on the use of the wild bootstrap are discussed. These do not require the practitioner to specify a parametric model for volatility, or to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. We formally establish the conditions under which these methods are asymptotically valid. A Monte Carlo simulation study demonstrates that significant improvements in finite sample size can be obtained by the bootstrap over the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments. An application to the term structure of interest rates in the US illustrates the difference between standard and bootstrap inferences regarding hypotheses on the co-integrating vectors and adjustment coefficients.
Classification-JEL: C30, C32
Keywords: Co-integration, adjustment coefficients, (un)conditional heteroskedasticity, heteroskedasticity-robust inference, wild bootstrap
File-Url: https://papers.tinbergen.nl/13187.pdf
File-Format: application/pdf
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Handle: RePEc:tin:wpaper:20130187