Likelihood Analysis of Seasonal Cointegration

TY - JOUR

T1 - Likelihood Analysis of Seasonal Cointegration

AU - Johansen, Søren

AU - Schaumburg, Ernst

N1 - JEL classification codes: C32

PY - 1999

Y1 - 1999

N2 - The error correction model for seasonal cointegration is analyzed. Conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given. The likelihood function is analyzed and the numerical calculation of the maximum likelihood estimators is discussed. The asymptotic distribution of the likelihood ratio test for cointegrating rank is given. It is shown that the estimated cointegrating vectors are asymptotically mixed Gaussian. The results resemble the results for cointegration at zero frequency when expressed in terms of a complex Brownian motion. Tables are provided for asymptotic inference.

AB - The error correction model for seasonal cointegration is analyzed. Conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given. The likelihood function is analyzed and the numerical calculation of the maximum likelihood estimators is discussed. The asymptotic distribution of the likelihood ratio test for cointegrating rank is given. It is shown that the estimated cointegrating vectors are asymptotically mixed Gaussian. The results resemble the results for cointegration at zero frequency when expressed in terms of a complex Brownian motion. Tables are provided for asymptotic inference.

KW - Faculty of Social Sciences

KW - autoregressive process

KW - Granger’s theorem

KW - error correction model

KW - complex Brownian motion

U2 - 10.1016/S0304-4076(98)00035-9

DO - 10.1016/S0304-4076(98)00035-9

M3 - Journal article

SN - 0304-4076

VL - 88

SP - 301

EP - 339

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -