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What is the Vector Error Correction Model?
The Vector Error Correction Model (VECM) is an econometric model used to analyze the long-term equilibrium relationship and short-term dynamics between multiple time series variables. It extends the Autoregressive Moving Average (ARMA) model to account for both the short-run deviations from equilibrium and the long-run equilibrium relationship among the variables. VECM has various applications in economics, finance, and time series analysis. It is widely used to analyze relationships among economic variables, such as exchange rates, interest rates, GDP components, and asset prices.
Here are the key aspects of the Vector Error Correction Model:
Cointegration: VECM is employed when the time series variables under consideration are cointegrated. Cointegration occurs when there is a long-term equilibrium relationship among the variables, even though they may exhibit short-term deviations from this equilibrium. It is a useful concept for analyzing non-stationary variables that have a stable long-term relationship.
Error Correction Term: VECM includes an error correction term that adjusts for short-term deviations from the long-run equilibrium relationship. This term captures the speed at which the variables adjust back to equilibrium after a shock or disturbance. It reflects the idea that any deviation from equilibrium will be corrected over time.
Stationarity and Differencing: VECM typically operates on differenced variables to ensure stationarity. By differencing the variables, non-stationary components are removed, allowing for the analysis of the stationary residual series. Differencing also facilitates the interpretation of the error correction term, which represents the adjustment process towards equilibrium.
Estimation and Inference: Estimating a VECM involves estimating the parameters through maximum likelihood or least squares methods. Hypothesis testing and inference are conducted based on standard statistical tests, such as t-tests, F-tests, or likelihood ratio tests, to assess the significance of coefficients, test for cointegration, and examine the stability of the model.
Granger Causality and Forecasting: VECM enables the analysis of Granger causality, which examines the causal relationships among the variables. It helps determine the direction and significance of the relationships between variables in both the short and long run. VECM can also be utilized for forecasting future values of the variables based on the estimated model parameters.
VECM is covered in more detail in module 6 of the CQF program.