Error Correction Factor Models For High Dimensional Cointegrated Time
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. Tu, Yundong, Yao, Qiwei ORCID: 0000-0003-2065-8486 and Zhang, Rongmao (2020) Error-correction factor models for high-dimensional cointegrated time series. Statistica Sinica, 30 (3).
1463 - 1484. ISSN 1017-0405 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 short-run 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.
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Abstract: Cointegration Inferences Often Rely On A Correct Specification For
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 ...
The Proposed Error-correction Factor Model Does Not Require An Explicit
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 ...
Cointegration Implies That While Individual Time Series May Be Non-stationary,
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 bot...
An Error Correction Model (ECM) Is Specifically Designed To Handle
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 t...
1463 - 1484. ISSN 1017-0405 Cointegration Inferences Often Rely On
1463 - 1484. ISSN 1017-0405 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...