Department of Economics and Business Economics

An extension of cointegration to fractional autoregressive processes

Research output: Working paperResearch

Standard

An extension of cointegration to fractional autoregressive processes. / Johansen, Søren.

Aarhus : CREATES, Institut for Økonomi, Aarhus Universitet, 2011.

Research output: Working paperResearch

Harvard

Johansen, S 2011 'An extension of cointegration to fractional autoregressive processes' CREATES, Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Johansen, S. (2011). An extension of cointegration to fractional autoregressive processes. Aarhus: CREATES, Institut for Økonomi, Aarhus Universitet.

CBE

Johansen S. 2011. An extension of cointegration to fractional autoregressive processes. Aarhus: CREATES, Institut for Økonomi, Aarhus Universitet.

MLA

Johansen, Søren An extension of cointegration to fractional autoregressive processes. Aarhus: CREATES, Institut for Økonomi, Aarhus Universitet. 2011., 15 p.

Vancouver

Johansen S. An extension of cointegration to fractional autoregressive processes. Aarhus: CREATES, Institut for Økonomi, Aarhus Universitet. 2011 Feb 1.

Author

Johansen, Søren. / An extension of cointegration to fractional autoregressive processes. Aarhus : CREATES, Institut for Økonomi, Aarhus Universitet, 2011.

Bibtex

@techreport{249653b5d07a46b4b9147f9a3f43b717,
title = "An extension of cointegration to fractional autoregressive processes",
abstract = "This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional processes. The model allows the process X(t) to be fractional of order d and cofractional of order d-b>0; that is, there exist vectors beta for which beta'X(t) is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived without the Gaussian assumption, under suitable moment conditions. We assume that the initial values are bounded and show that they do not influence the asymptotic analysis The estimator of \beta is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. The asymptotic distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion.",
keywords = "Cofractional processes, cointegration rank, fractional cointegration, likelihood inference, vector autoregressive model.",
author = "S{\o}ren Johansen",
year = "2011",
month = "2",
day = "1",
language = "English",
publisher = "CREATES, Institut for {\O}konomi, Aarhus Universitet",
type = "WorkingPaper",
institution = "CREATES, Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - An extension of cointegration to fractional autoregressive processes

AU - Johansen, Søren

PY - 2011/2/1

Y1 - 2011/2/1

N2 - This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional processes. The model allows the process X(t) to be fractional of order d and cofractional of order d-b>0; that is, there exist vectors beta for which beta'X(t) is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived without the Gaussian assumption, under suitable moment conditions. We assume that the initial values are bounded and show that they do not influence the asymptotic analysis The estimator of \beta is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. The asymptotic distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion.

AB - This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional processes. The model allows the process X(t) to be fractional of order d and cofractional of order d-b>0; that is, there exist vectors beta for which beta'X(t) is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived without the Gaussian assumption, under suitable moment conditions. We assume that the initial values are bounded and show that they do not influence the asymptotic analysis The estimator of \beta is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. The asymptotic distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion.

KW - Cofractional processes, cointegration rank, fractional cointegration, likelihood inference, vector autoregressive model.

M3 - Working paper

BT - An extension of cointegration to fractional autoregressive processes

PB - CREATES, Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -