# Tag Info

### Why Are Impulse Responses in VECM Permanent?

This is a great question, and I'm learning so bear with me. What would be a correct interpretation of an impulse response that does not go back to 0 in a VECM? Riffing on the drunken walk theme, ...
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### Prediction from VECM in R using external forecasts of regressors

You can simply use the newdata argument of the predict method. Note that if you have a VECM with three lags, lags in tsDyn refer ...
• 3,083
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### Cointegration relations - What is the intuition?

I find a constructive example easier than deductive ones, so here it is. Suppose there is a unit-root process $x_t$. It could be the price of a company's share on a stock exchange, for example. ...
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### VAR model for first differences (not a good idea?)

Think of it this way, when data is I(1), that is interesting. It tell's us something about the underlying process. Further, if you have two I(1) process and they are co-integrated, then this is ...
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### VECM: alpha is a 0-vector? cointegration rank = $k$ even though $X_t$ is I(1)?

A brief answer: You logic is correct. In theory, this should not happen. In practice, this may be caused by estimation imprecision and/or low power of tests. In theory, the lag does not matter. As ...
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### Selecting lag order for VAR and VECM

Your methodology seems fine. From a theoretical perspective, it broadly agrees with recommendations in time series textbooks. From an empirical perspective, your models have well-behaved residuals, ...
• 68.1k
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### Testing for cointegration and building a VEC model

You seem to be doing pairwise analysis when you in fact have three variables. This way you may miss cointegrating relationships that are not pairwise but involve more variables. The standard way in ...
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### How to forecast from VECM (in R)?

If you are interested in forecasting (as you state in the beginning and repeat multiple times) rather than making inference (which you mention once), then estimating a VECM, transforming it into a ...
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### Sign of adjustment coefficient of error correction term in VECM

This need not imply divergence. Here is an example of where two positive and one negative loading on the error correction term makes intuitive sense. This can be trivially extended to $m>2$ ...
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### Do all variables in a VAR/VEC need to be normally distributed, or only the target variable?

Unless the assumptions of regression modeling have changed, there is no stipulation about the distributions of the variables in the model -- normal or otherwise. There are some technical assumptions ...
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### Estimation of a VEC model in R (standard errors)

You can use package tsDyn for this, function VECM, and summary() on that output: ...
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### VAR lag length vs Johansen cointegration test outcome?

This is a usual problem with the two steps procedure, where one selects first the lag, then the cointegration rank depending on the lag chose in the first step. Puzzle 1: The claim that the lag ...
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### Is ARCH test mandatory for VAR?

Is ARCH test mandatory for VAR? "Mandatory" is a strong word when it comes to statistical practice. I would say, ARCH test is advisable, as is any relevant diagnostic test. Extra diagnostic testing ...
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### Does using difference transformation lead to bias? (Levels vs differences regression)

And here is the answer, via simulation. Perhaps someone can come up with a mathematical proof to boot. The R code: ...
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### VAR or VECM for a mix of stationary and nonstationary variables?

Should I use VAR or VECM to find relation between them? In practice, it depends on the power of cointegration tests: If your variables are cointegrated and you used a VAR model: you could have done ...
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### Why do we need a VECM specification if the I(1) processes are cointegrated?

To formalize and generalize dlnB's +1 answer a little (based on Hamilton's textbook): Cointegration implies that the deviations from the equilibrium are $I(0)$. Hence, some mechanism must bring back ...
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### Goodness of fit of vector error correction model (VECM)

If you got low $R^2$ when the response variable is the first difference of an integrated variable (which I understand is the case), then it is as expected; if you had got that when the response ...
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### Cointegration Restrictions

You are testing whether restrictions within a VECM hold, which is not directly related to testing for cointegration. These are two different things. If the series are not cointegrated, you are ...
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