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6 votes

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, ...
Ben Ogorek's user avatar
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6 votes

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 ...
Matifou's user avatar
  • 3,083
6 votes
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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. ...
Richard Hardy's user avatar
6 votes

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 ...
Jacob H's user avatar
  • 922
6 votes
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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 ...
Richard Hardy's user avatar
5 votes
Accepted

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, ...
Richard Hardy's user avatar
4 votes
Accepted

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 ...
Richard Hardy's user avatar
4 votes

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 ...
Richard Hardy's user avatar
4 votes

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 $m>2$ ...
Richard Hardy's user avatar
4 votes

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 ...
user78229's user avatar
  • 10.8k
4 votes

Estimation of a VEC model in R (standard errors)

You can use package tsDyn for this, function VECM, and summary() on that output: ...
Matifou's user avatar
  • 3,083
3 votes
Accepted

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 ...
Matifou's user avatar
  • 3,083
3 votes

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 ...
Richard Hardy's user avatar
3 votes
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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: ...
Dole's user avatar
  • 943
3 votes

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 ...
rmojab63's user avatar
  • 216
3 votes
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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 ...
Christoph Hanck's user avatar
2 votes

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 ...
Richard Hardy's user avatar
2 votes
Accepted

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 ...
Richard Hardy's user avatar
2 votes
Accepted

Error correction term has both positive and negative loadings - is that OK?

There is nothing wrong with the error correction term having positive loadings in some equations and negative in other. In fact, you could construct an example yourself. Take $y_{1,t}=\sum_{\tau=1}...
Richard Hardy's user avatar
2 votes
Accepted

How to check stability condition of VEC estimates in R?

One way to check for stability is obtaining the roots of the determinant (using eigen) of the companion matrices of lagged endogenous variables that you obtain by ...
Lucas Farias's user avatar
  • 1,402
2 votes
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Build a VECM model for stock price prediction and interpreting output

Yes, because many models assume the variables are stationary. When the assumption is violated, the fitted model might not make sense (e.g. the left hand side would diverge from the right hand side ...
Richard Hardy's user avatar
2 votes
Accepted

Does existence of Cointegration mean that VECM is preferred to VAR?

If your original or logarithmically-transformed variables are I(1) and cointegrated, then VECM is the correct model. Unrestricted VAR in levels is misspecified due to missing restrictions because of ...
Richard Hardy's user avatar
2 votes
Accepted

If a DGP is ARIMA(P,D,0) does that imply no other variables affect this process?

If we interpret your claim as "if an ARIMA process has no MA part, then it is independent of every other stochastic process", the answer is decidedly no. As I said above, just take two correlated ...
Chris Haug's user avatar
  • 5,850
2 votes

Using a VAR over a VECM (in spite of of existing cointegration)

There is at least one reason -- the bias-variance trade-off. You might prefer a wrong model as long as it gives you better forecasts. Suppose VECM is the true model. Then VAR in first differences is ...
Richard Hardy's user avatar
2 votes

The role of Granger causality in VAR/VECM model selection

As far as I know, Granger causality on its own is not typically used in economics for model-building. Cointegration is more widely used, where time series tests like the ADF and Johansen tests are ...
A. G.'s user avatar
  • 2,151
2 votes

VECM in matrix form - explanation

All is fine with your explanation. The 2x2 matrix with $\delta$ and $\rho$ terms are coefficients in front of the lagged series $\Delta Y_{t−i}$ and $\Delta X_{t−i}$. Without it, these lags would ...
Richard Hardy's user avatar
2 votes
Accepted

Can I use a VAR in first differences despite having co-integrated data?

Hi: ( Note that below considers the bivariate case but same type of discussion holds in general for $n > 2$ ). The impulse response function using the var in differences will not be correct ...
mlofton's user avatar
  • 2,527
2 votes

Interpreting the names used in the output of Johansen test in package urca in R

Consider a VAR with k I(1) variables $\mathbf{X_t}$ and $p$ lags . If there is cointegration the VAR can be written $$\mathbf{X_t} = \sum_{i=1}^p \mathbf{\Pi_iX_t + \varepsilon_t} $$ subject to ...
user1483's user avatar
  • 176
2 votes
Accepted

Vector error correction model output

The first r columns of the loading matrix gives you $\alpha$. You can also get all the coefficients for the VECM easily with the cajorls() function: ...
Matt P's user avatar
  • 644
2 votes

How to remove seasonality?

In your data, we can see a clear trend in the series - aside from the peaks and valleys that we observe due to seasonality. In this regard, given that you are trying to test cointegration - examining ...
Michael Grogan's user avatar

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