Likelihood analysis of the I(2) model

Søren Johansen

doi:10.1111/1467-9469.00074

Likelihood analysis of the I(2) model

88 Citations (Scopus)

Abstract

The I(2) model is defined as a submodel of the general vector autoregressive model, by two reduced rank conditions. The model describes stochastic processes with stationary second difference. A parametrization is suggested which makes likelihood inference feasible. Consistency of the maximum likelihood estimator is proved, and the asymptotic distribution of the maximum likelihood estimator is given. It is shown that the asymptotic distribution is either Gaussian, mixed Gaussian or, in some cases, even more complicated.

Original language	English
Journal	Scandinavian Journal of Statistics
Volume	24
Issue number	4
Pages (from-to)	433-462
Number of pages	30
ISSN	0303-6898
DOIs	https://doi.org/10.1111/1467-9469.00074
Publication status	Published - 1997

Keywords

Faculty of Social Sciences
cointegration
integrated processes
time series analysis
vector autoregressive processes

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10.1111/1467-9469.00074

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title = "Likelihood analysis of the I(2) model",

abstract = "The I(2) model is defined as a submodel of the general vector autoregressive model, by two reduced rank conditions. The model describes stochastic processes with stationary second difference. A parametrization is suggested which makes likelihood inference feasible. Consistency of the maximum likelihood estimator is proved, and the asymptotic distribution of the maximum likelihood estimator is given. It is shown that the asymptotic distribution is either Gaussian, mixed Gaussian or, in some cases, even more complicated.",

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AB - The I(2) model is defined as a submodel of the general vector autoregressive model, by two reduced rank conditions. The model describes stochastic processes with stationary second difference. A parametrization is suggested which makes likelihood inference feasible. Consistency of the maximum likelihood estimator is proved, and the asymptotic distribution of the maximum likelihood estimator is given. It is shown that the asymptotic distribution is either Gaussian, mixed Gaussian or, in some cases, even more complicated.

KW - Faculty of Social Sciences

KW - cointegration

KW - integrated processes

KW - time series analysis

KW - vector autoregressive processes

U2 - 10.1111/1467-9469.00074

DO - 10.1111/1467-9469.00074

M3 - Journal article

SN - 0303-6898

VL - 24

SP - 433

EP - 462

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

IS - 4

ER -

Likelihood analysis of the I(2) model

Abstract

Keywords

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