Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

TY - UNPB

T1 - Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

AU - Cavaliere, Guiseppe

AU - Rahbæk, Anders

AU - Taylor, A.M. Robert

PY - 2008

Y1 - 2008

N2 - Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.

AB - Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice.

KW - Co-integration, non-stationary volatility, trace and maximum eigenvalue tests, wild bootstrap

M3 - Working paper

BT - Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -