Error Correction Factor Models Docslib

Leo Migdal

-Dec 14, 2025, 3:32 PM

Abstract: Cointegration inferences often rely on a correct specification for the short-run dynamic vector autoregression. However, this specification is unknown, a priori. A lag length that is too small leads to an erroneous inference as a result of the misspecification. In contrast, using too many lags leads to a dramatic increase in the number of parameters, especially when the dimension of the time series is high. In this paper, we develop a new methodology which adds an error-correction term for the long-run equilibrium to a latent factor model in order to model the shortrun dynamic relationship. The inferences use the eigenanalysis-based methods to estimate the cointegration and latent factor process.

The proposed error-correction factor model does not require an explicit specification of the short-run dynamics, and is particularly effective for high-dimensional cases, in which the standard error-correction suffers from overparametrization. In addition, the model improves the predictive performance of the pure factor model. The asymptotic properties of the proposed methods are established when the dimension of the time series is either fixed or diverging slowly as the length of the time series goes to infinity. Lastly, the performance of the model is evaluated using both simulated and real data sets. Key words and phrases: Cointegration, eigenanalysis, factor models, nonstationary processes, vector time series. An Error Correction Model (ECM) is a powerful econometric tool used to model the relationship between non-stationary time series variables that are cointegrated.

Cointegration implies that while individual time series may be non-stationary, a linear combination of them is stationary, indicating a long-run equilibrium relationship. ECMs are particularly useful for capturing both short-term dynamics and long-term equilibrium adjustments between variables. An Error Correction Model (ECM) is specifically designed to handle non-stationary data by addressing both short-term dynamics and long-term equilibrium relationships between time series variables. The term "error correction" refers to the mechanism by which deviations from the long-run equilibrium are corrected over time. In an ECM, the error correction term represents the extent to which the previous period's disequilibrium influences the current period's adjustments. This allows the model to capture both short-term fluctuations and the speed at which the variables return to equilibrium.

An Error Correction Model (ECM) is specifically designed to handle non-stationary data by addressing both short-term dynamics and long-term equilibrium relationships between time series variables. Non-stationary data are time series that have properties such as mean, variance, and autocorrelation that change over time. When dealing with non-stationary data, traditional regression models can lead to spurious results. However, if two or more non-stationary series are cointegrated, it means they share a common stochastic trend and move together in the long run, despite being non-stationary individually. All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions.

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This article delves into the technical aspects of ECM, its applications, estimation methods, and limitations. An Error Correction Model (ECM) belongs to a category of multiple time series models designed to handle data where the underlying variables share a long-run common stochastic trend, also known as cointegration. The primary concept behind ECM is that deviations from long-term equilibrium are corrected gradually through short-term adjustments. This makes ECMs particularly useful for analyzing both short-term dynamics and long-term relationships between variables. ECMs are crucial for forecasting future values of a time series by incorporating both long-term equilibrium relationships and short-term dynamics, providing more accurate and nuanced predictions. At the heart of ECMs lies the concept of cointegration.

Cointegrated time series share a long-term equilibrium relationship, even if they individually exhibit non-stationary behavior. This implies that a linear combination of these series is stationary. Cointegration signifies that the series move together in the long run, although they might deviate in the short term. The Engle and Granger two-step approach is a widely used method for estimating ECMs:

Error Correction Factor Models Docslib

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When Requesting A Correction, Please Mention This Item's Handle: RePEc:ehl:lserod:106994.