Size and power of the likelihood ratio test for seasonal cointegration in small samples: A Monte Carlo study

This paper investigates the small sample size and power properties of the likelihood ratio test in the seasonal error correction model. Two specifications of the model at the annual frequency are analyzed. One is more restricted (RS), designed for the particular case of 'synchronous cointegration', whereas the other specification is general (GS). The results indicate that RS has poor size properties in cases where non-synchronous cointegration clearly should play a role. There is a risk of finding 'evidence' of too many cointegrating vectors at the annual frequency when using RS. On the other hand, if the restriction is almost satisfied, the general specification looses power at least for small sample sizes, while tests in RS have good properties. The number of true cointegration relations at one certain frequency affect the test for the rank at other frequencies in small samples. This result suggests a possible gain in efficiency when testing at a certain frequency, by concentrating out the 'correct' number of vectors at the other frequencies.