Likelihood Inference for a Nonstationary Fractional Autoregressive Model
Publikation: Working paper › Forskning
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Likelihood Inference for a Nonstationary Fractional Autoregressive Model. / Johansen, Søren; Nielsen, Morten Ørregaard.
Department of Economics, University of Copenhagen, 2007.Publikation: Working paper › Forskning
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TY - UNPB
T1 - Likelihood Inference for a Nonstationary Fractional Autoregressive Model
AU - Johansen, Søren
AU - Nielsen, Morten Ørregaard
N1 - JEL Classification: C22
PY - 2007
Y1 - 2007
N2 - This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II
AB - This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II
KW - Faculty of Social Sciences
KW - Dickey-Fuller test
KW - fractional unit root
KW - likelihood inference
M3 - Working paper
BT - Likelihood Inference for a Nonstationary Fractional Autoregressive Model
PB - Department of Economics, University of Copenhagen
ER -
ID: 1523903