Vector Error Correction Model – Why Use VECM for Time Series Analysis

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I am confused about the Vector Error Correction Model (VECM).

Technical background:
VECM offers a possibility to apply Vector Autoregressive Model (VAR) to integrated multivariate time series. In the textbooks they name some problems in applying a VAR to integrated time series, the most important of which is the so called spurious regression (t-statistics are highly significant and R^2 is high although there is no relation between the variables).

The process of estimating the VECM consists roughly of the three following steps, the confusing one of which is for me the first one:

  1. Specification and estimation of a VAR model for the integrated multivariate time series

  2. Calculate likelihood ratio tests to determine the number of cointegration relations

  3. After determining the number of cointegrations, estimate the VECM

In the first step one estimates a VAR model with appropriate number of lags (using the usual goodness of fit criteria) and then checks if the residuals correspond to the model assumptions, namely the absence of serial correlation and heteroscedasticity and that the residuals are normally distributed. So, one checks if the VAR model appropriately describes the multivariate time series, and one proceeds to further steps only if it does.

And now to my question: If the VAR model describes the data well, why do I need the VECM at all? If my goal is to generate forecasts, isn't it enough to estimate a VAR and check the assumptions, and if they are fulfilled, then just use this model?

Best Answer

The foremost advantage of VECM is that it has nice interpretation with long term and short term equations.

In theory VECM is just a representation of cointegrated VAR. This representation is courtesy of Granger's representation theorem. So if you have cointegrated VAR it has VECM representation and vice versa.

In practice you need to determine the number of cointegrating relationships. When you fix that number you restrict certain coefficients of VAR model. So advantage of VECM over VAR (which you estimate ignoring VECM) is that the resulting VAR from VECM representation has more efficient coefficient estimates.

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