TY - JOUR
T1 - Testing for co-integration in vector autoregressions with non-stationary volatility
AU - Cavaliere, Giuseppe
AU - Rahbek, Anders Christian
AU - Taylor, Robert M.
N1 - JEL classification: C30, C32
PY - 2010
Y1 - 2010
N2 - Many key macroeconomic and financial variables are characterized 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) and (Johansen, 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, or 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 macroeconomic and financial variables are characterized 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) and (Johansen, 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, or 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 - Faculty of Social Sciences
KW - co-integration
KW - non-stationary volatility
KW - trace and maximum eigenvalue tests
KW - wild bootstrap
U2 - 10.1016/j.jeconom.2010.03.003
DO - 10.1016/j.jeconom.2010.03.003
M3 - Journal article
SN - 0304-4076
VL - 158
SP - 7
EP - 24
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -