Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

TY - JOUR

T1 - Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models

AU - Cavaliere, Giuseppe

AU - Nielsen, Heino Bohn

AU - Rahbek, Anders

PY - 2015/3/1

Y1 - 2015/3/1

N2 - It is well known that the finite-sample properties of tests of hypotheses on the co-integrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett-type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic χ2 tests fail most severely. In this paper, we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co-integration rank (Cavaliere, Rahbek, and Taylor, 2012), establishing the validity of the bootstrap in the framework of hypotheses on the co-integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein-Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.

AB - It is well known that the finite-sample properties of tests of hypotheses on the co-integrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett-type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic χ2 tests fail most severely. In this paper, we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co-integration rank (Cavaliere, Rahbek, and Taylor, 2012), establishing the validity of the bootstrap in the framework of hypotheses on the co-integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein-Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.

U2 - 10.3982/ecta11952

DO - 10.3982/ecta11952

M3 - Journal article

SN - 0012-9682

VL - 83

SP - 813

EP - 831

JO - Econometrica

JF - Econometrica

IS - 2

ER -