TY - JOUR
T1 - Likelihood inference for a nonstationary fractional autoregressive model
AU - Johansen, Søren
AU - Ørregård Nielsen, Morten
N1 - JEL classification: C22
PY - 2010/9
Y1 - 2010/9
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,⋯,XT 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 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 these results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of 12
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,⋯,XT 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 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 these results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of 12
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
SN - 0304-4076
VL - 158
SP - 51
EP - 66
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -