Arbeitspapier
Likelihood inference for a nonstationary fractional autoregressive model
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 X_{1},...,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 < b < d < inf.}, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis. The limit distributions contain the fractional Brownian motion of type II.
- Sprache
-
Englisch
- Erschienen in
-
Series: Queen's Economics Department Working Paper ; No. 1172
- Klassifikation
-
Wirtschaft
Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- Thema
-
Dickey-Fuller test
fractional unit root
likelihood inference
Zeitreihenanalyse
Autokorrelation
Unit Root Test
Maximum-Likelihood-Methode
Modellierung
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Johansen, Søren
Nielsen, Morten Ørregaard
- Ereignis
-
Veröffentlichung
- (wer)
-
Queen's University, Department of Economics
- (wo)
-
Kingston (Ontario)
- (wann)
-
2008
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:44 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Johansen, Søren
- Nielsen, Morten Ørregaard
- Queen's University, Department of Economics
Entstanden
- 2008
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