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Keywords
(11)
Asymptotic Distribution
Autoregressive Process
Error Correction Model
Maximum Likelihood Estimate
Nonstationary Time Series
Social Science
Statistical Analysis
Unit Root
Vector Autoregressive Process
Data Generation Process
Likelihood Ratio Test
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Statistical analysis of cointegration vectors
Statistical analysis of cointegration vectors,10.1016/01651889(88)900413,Journal of Economic Dynamics & Control,Soren Johansen
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Statistical analysis of cointegration vectors
(
Citations: 2827
)
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Soren Johansen
We consider a nonstationary
vector autoregressive process
which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the
maximum likelihood
estimator of the space of cointegration vectors and the
likelihood ratio test
of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors. The
asymptotic distribution
of these test statistics are found and the first is described by a natural multivariate version of the usual test for
unit root
in an autoregressive process, and the other is a x2 test. 1. Introduction The idea of using cointegration vectors in the study of
nonstationary time series
comes from the work of Granger (1981), Granger and Weiss (1983), Granger and Engle (1985), and Engle and Granger (1987). The connection with error correcting models has been investigated by a number of authors; see Davidson (1986), Stock (1987), and Johansen (1988) among others. Granger and Engle (1987) suggest estimating the cointegration relations using regression, and these estimators have been investigated by Stock (1987), Phillips (1985), Phillips and Durlauf (1986), Phillips and Park (1986a, b, 1987), Phillips and Ouliaris (1986,1987), Stock and Watson (1987), and Sims, Stock and Watson (1986). The purpose of this paper is to derive
maximum likelihood
estimators of the cointegration vectors for an
autoregressive process
with independent Gaussian errors, and to derive a
likelihood ratio test
for the hypothesis that there is a given number of these. A similar approach has been taken by Ahn and Reinsel (1987). This program will not only give good estimates and test statistics in the Gaussian case, but will also yield estimators and tests, the properties of which can be investigated under various other assumptions about the underlying data generating process. The reason for expecting the estimators to behave better *The simulations were carefully performed by Marc Andersen with the support of the Danish
Social Science
Research Council. The author is very grateful to the referee whose critique of the first version greatly helped improve the presentation.
Journal:
Journal of Economic Dynamics & Control  J ECON DYN CONTROL
, vol. 12, no. 23, pp. 231254, 1988
DOI:
10.1016/01651889(88)900413
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Citation Context
(601)
...The standard approach used to test for cointegration is the linear Full Information Maximum Likelihood (FIML) technique of
Johansen (1988, 1991)
...
Camilo Serrano
,
et al.
Fractional Cointegration Analysis of Securitized Real Estate
...Given asymmetric adjustments, dynamic relations implicit in tests of the Dutch disease hypothesis based on traditional methods of Engle and Granger (1987),
Johansen (1988)
and Pesaran et al. (2001) are misspecified...
Hassan Mohammadi
,
et al.
Oil prices and exchange rates in oilexporting countries: evidence fro...
...
Johansen (1988)
’s methodology based on multivariate vector autoregressive (VAR) model has provided researcher necessary tools for multivariate cointegration tests and error corrections...
...The second approach, due to
Johansen (1988, 1991)
and Stock and Watson (1988), is based on the VAR approach...
...
Johansen (1988)
and Johansen and Juselius (1990) developed a maximum likelihood ratio test that allows testing for multiple cointegration vectors in a multivariate setting...
Richard Fu
,
et al.
On the cointegration of international stock indices
...
Johansen (1988)
developed a likelihood ratio test for cointegration; Johansen and...
Rolando F. Peláez
.
The housing bubble in realtime: the end of innocence
...where the eigenvalues ~ 0 s are obtained by solving a generalised eigenvalue problem, along the lines of
Johansen (1988)
...
Nikolaos Giannellis
,
et al.
Behavioural equilibrium exchange rate and total misalignment: evidence...
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Sort by:
Citations
(2827)
Fractional Cointegration Analysis of Securitized Real Estate
(
Citations: 1
)
Camilo Serrano
,
Martin Hoesli
Journal:
Journal of Real Estate Finance and Economics  J REAL ESTATE FINANC ECON
, vol. 41, no. 1, pp. 120, 2012
Oil prices and exchange rates in oilexporting countries: evidence from TAR and MTAR models
(
Citations: 1
)
Hassan Mohammadi
,
Mohammad R. JahanParvar
Journal:
Journal of Economics and Finance
, pp. 114, 2012
Explaining house price changes in Greece
(
Citations: 1
)
Dimitrios Gounopoulos
,
Andreas G. Merikas
,
Anna A. Merika
,
Anna Triantafyllou
Journal:
Applied Financial Economics
, vol. 22, no. 7, pp. 549561, 2012
On the cointegration of international stock indices
Richard Fu
,
Marco Pagani
Journal:
Journal of Economics and Finance
, vol. 34, no. 1, pp. 118, 2012
The housing bubble in realtime: the end of innocence
Rolando F. Peláez
Journal:
Journal of Economics and Finance
, pp. 115, 2012