Co-integration and error correction: representation, estimation and testing

@article{Engle1987CointegrationAE,
  title={Co-integration and error correction: representation, estimation and testing},
  author={Robert F. Engle and Clive William John Granger},
  journal={Econometrica},
  year={1987},
  volume={55},
  pages={251-276}
}
The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of time series is said to be cointegrated with cointegrating vector a if each element is stationary only after differencing while linear combinations a8xt are themselves stationary. A representation theorem connects the moving average , autoregressive, and error correction representations for… 

Tables from this paper

Examining impulse response functions in cointegrated systems

A system of reduced forms with cointegrated variables may be estimated in two ways: as a vector autoregression in levels, or as a vector error correction model. The latter is a restricted version of

Cointegration and Error Correction Mechanisms

Starting from a multivariate Wold representation for N variables that are integrated of order 1, this paper shows that, given that the N variables have r cointegrating vectors, there is an

The Power of Cointegration Tests

A cointegration test statistic based upon estimation of an error-correction model can be approximately normally distributed when no cointegration is present. By contrast, the equivalent Dickey-Fuller

A new instrumental variable approach for estimation and testing in fractional cointegrating regressions

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocorrelation and the crosscorrelation functions of the

Residuals-based Tests for Cointegration: An Analytical Comparison

This paper compares five residuals-based tests for the null of no cointegration to identify which unit root test should be used when testing for cointegration. The tests are compared in terms of

Polynomial cointegration estimation and test

Stationary Vector Autoregressive Representation of Error Correction Models

The paper introduces a stationary vector autoregressive (VAR) representation of the error correction model (ECM). This representation explicitly regards the cointegration error a dependent variable,

Panel Error Correction Testing with Common

This paper considers a cointegrated panel data model with common factors. Starting from the triangular representation of the model a Granger type representation theorem is derived. The conditional

Dynamic specification and cointegration

Augmenting a first-order dynamic regression model by adding particular redundant regressors gives a least-squares estimator of the lagged-dependent variable coefficient that is independent of
...

References

SHOWING 1-10 OF 37 REFERENCES

Forecasting and testing in co-integrated systems

Multiple Time Series Regression with Integrated Processes

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst

The Mathematical Structure of Error Correction Models.

TLDR
A general error Correction model is defined, that encompasses the usual error correction model as well as the integral correction model by allowing a finite number of error correction terms which correspond to linear combinations of the vector process that are integrated of different order.

Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors

Time series variables that stochastically trend together form a cointegrated system. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to the

Time series regression with a unit root

This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression

Error Correction Mechanisms

TLDR
This paper examines the surprisingly strong arguments that exist in terms of economic theory, for the use of error correction mechanisms in the specification of short run dynamic adjustment.

Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk

This paper considers the null hypothesis that the errors on a regression equation form a random walk. By using the standard Durbin-Watson assumptions, we derive three test statistics that are

Distribution of the Estimators for Autoregressive Time Series with a Unit Root

Abstract Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with