TY - JOUR

T1 - Likelihood inference for a nonstationary fractional autoregressive model

AU - Johansen, Søren

AU - Ørregård Nielsen, Morten

N1 - JEL classification: C22

PY - 2010

Y1 - 2010

N2 - This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions.We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2

AB - This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions.We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2

KW - Faculty of Social Sciences

KW - Dickey–Fuller test

KW - fractional unit root

KW - likelihood inference

U2 - 10.1016/j.jeconom.2010.03.006

DO - 10.1016/j.jeconom.2010.03.006

M3 - Journal article

VL - 158

SP - 51

EP - 66

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -