@ARTICLE{16360361_1987,
author = {Engle, Robert F. and Granger , Clive W. J.},
keywords = {cointegrating vector, estimation, monte carlo method, time series, unit root, математический метод, метод Монте-Карло, эконометрический метод},
title = {Co-integration and Error Correction: Representation, Estimation and
Testing },
journal = {Econometrica},
year = {1987},
month = {},
volume = {55},
number = {2},
pages = {251-276},
url = {http://ecsocman.hse.ru/text/16360361/},
publisher = {},
language = {ru},
abstract = {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 series 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 M1, M3, or aggregate liquid assets. },
annote = {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 series 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 M1, M3, or aggregate liquid assets. }
}