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# Error correction model

About: Error correction model is a research topic. Over the lifetime, 4590 publications have been published within this topic receiving 113812 citations.

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TL;DR: 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.

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.

27,170 citations

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TL;DR: In this paper, the estimation and testing of long-run relations in economic modeling are addressed, starting with a vector autoregressive (VAR) model, the hypothesis of cointegration is formulated as a hypothesis of reduced rank of the long run impact matrix.

Abstract: The estimation and testing of long-run relations in economic modeling are addressed. Starting with a vector autoregressive (VAR) model, the hypothesis of cointegration is formulated as the hypothesis of reduced rank of the long-run impact matrix. This is given in a simple parametric form that allows the application of the method of maximum likelihood and likelihood ratio tests. In this way, one can derive estimates and test statistics for the hypothesis of a given number of cointegration vectors, as well as estimates and tests for linear hypotheses about the cointegration vectors and their weights. The asymptotic inferences concerning the number of cointegrating vectors involve nonstandard distributions. Inference concerning linear restrictions on the cointegration vectors and their weights can be performed using the usual chi squared methods. In the case of linear restrictions on beta, a Wald test procedure is suggested. The proposed methods are illustrated by money demand data from the Danish and Finnish economies.

12,449 citations

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TL;DR: In this article, the authors compared several methods (ordinary least squares, nonlinear least square, maximum likelihood in an error correction model, principal components, and canonical correlations) of estimating cointegrating vectors.

1,218 citations

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TL;DR: In this article, a bivariate error correction model with a GARCH error structure was proposed to estimate the risk-minimizing futures hedge ratios for several currencies and a dynamic hedging strategy was proposed in which the potential risk reduction is more than enough to offset the transactions costs for most investors.

Abstract: Most research on hedging has disregarded both the long-run cointegrating relationship between financial assets and the dynamic nature of the distributions of the assets. This study argues that neglecting these affects the hedging performance of the existing models and proposes an alternative model that accounts for both of them. Using a bivariate error correction model with a GARCH error structure, the risk-minimizing futures hedge ratios for several currencies are estimated. Both within-sample comparisons and out-of-sample comparisons reveal that the proposed model provides greater risk reduction than the conventional models. Furthermore, a dynamic hedging strategy is proposed in which the potential risk reduction is more than enough to offset the transactions costs for most investors.

1,182 citations