## Abstract

Determining the co-integrating rank of a system of variables has become a

fundamental aspect of applied research in macroeconomics and finance. It is wellknown

that standard asymptotic likelihood ratio tests for co-integration rank

of Johansen (1996) can be unreliable in small samples with empirical rejection

frequencies often very much in excess of the nominal level. As a consequence,

bootstrap versions of these tests have been developed. To be useful, however,

sequential procedures for determining the co-integrating rank based on these

bootstrap tests need to be consistent, in the sense that the probability of selecting

a rank smaller than (equal to) the true co-integrating rank will converge to

zero (one minus the marginal significance level), as the sample size diverges, for

general I(1) processes. No such likelihood-based procedure is currently known

to be available. In this paper we fill this gap in the literature by proposing

a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration

rank estimation for general I(1) processes. Finite sample Monte Carlo

simulations show the proposed procedure performs well in practice.

fundamental aspect of applied research in macroeconomics and finance. It is wellknown

that standard asymptotic likelihood ratio tests for co-integration rank

of Johansen (1996) can be unreliable in small samples with empirical rejection

frequencies often very much in excess of the nominal level. As a consequence,

bootstrap versions of these tests have been developed. To be useful, however,

sequential procedures for determining the co-integrating rank based on these

bootstrap tests need to be consistent, in the sense that the probability of selecting

a rank smaller than (equal to) the true co-integrating rank will converge to

zero (one minus the marginal significance level), as the sample size diverges, for

general I(1) processes. No such likelihood-based procedure is currently known

to be available. In this paper we fill this gap in the literature by proposing

a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration

rank estimation for general I(1) processes. Finite sample Monte Carlo

simulations show the proposed procedure performs well in practice.

Originalsprog | Engelsk |
---|---|

Udgivelsessted | Aarhus |

Udgiver | Institut for Økonomi, Aarhus Universitet |

Antal sider | 23 |

Status | Udgivet - 2010 |