Article

CO-INTEGRATION AND ERROR CORRECTION: REPRESENTATION, ESTIMATION, AND TESTING

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The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x, first achieves stationarity after differencing, but a linear combination a'x, is already stationary, the time series x, are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x, = 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a veries of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not Ml, M3, or aggregate liquid assets.

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Ketersediaan

Informasi Detail

Judul Seri

CO-INTEGRATION AND ERROR CORRECTION

No. Panggil

ATC LO ENG c

Penerbit

: JSTOR., 1987

Deskripsi Fisik

27 p.

Bahasa

English

ISBN/ISSN

-

Klasifikasi

LO

Tipe Isi

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Tipe Media

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Tipe Pembawa

online resource

Edisi

Vol. 55, No. 2 (March, 1987), 251-276

Subjek

co-integration
vector autoregression
unit roots
error correction
multivariate time series
Dickey-Fuller tests

Info Detail Spesifik

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Pernyataan Tanggungjawab

Robert F. Engle

Versi lain/terkait

Lampiran Berkas

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