Likelihood inference for a fractionally cointegrated vector autoregressive model
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Likelihood inference for a fractionally cointegrated vector autoregressive model. / Johansen, Søren; Ørregård Nielsen, Morten.
I: Econometrica, Bind 80, Nr. 6, 11.2012, s. 2667-2732.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Likelihood inference for a fractionally cointegrated vector autoregressive model
AU - Johansen, Søren
AU - Ørregård Nielsen, Morten
PY - 2012/11
Y1 - 2012/11
N2 - We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 01/2, we prove that the limit distribution of (ß',¿')' is mixed Gaussian and for the remaining parameters it is Gaussian. The limit distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion of type II extended by u^{-(d0-b0)}. If b0<1/2 all limit distributions are Gaussian or chi-squared.
AB - We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 01/2, we prove that the limit distribution of (ß',¿')' is mixed Gaussian and for the remaining parameters it is Gaussian. The limit distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion of type II extended by u^{-(d0-b0)}. If b0<1/2 all limit distributions are Gaussian or chi-squared.
KW - Faculty of Social Sciences
KW - Cofractional processes, cointegration rank, fractional cointegration, likelihood inference, vector autoregressive model
U2 - 10.3982/ECTA9299
DO - 10.3982/ECTA9299
M3 - Journal article
VL - 80
SP - 2667
EP - 2732
JO - Econometrica
JF - Econometrica
SN - 0012-9682
IS - 6
ER -
ID: 41860906