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I am using R vars package to implement VAR model in a multivariate time series model. I tried to run:

VAR(foo_ts, p = 6)

but I was getting this error message:

Error in solve.default(Sigma) : system is computationally singular: reciprocal condition number = 0

foo_ts is a time series data.

I have tried to adapt examples in stackexchange and stackoverflow but have not been successful in running the VAR model. I have successfully run the VAR model on other datasets but not on foo_ts. Any help will be appreciated.

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  • $\begingroup$ Have you tried looking up the error message online? $\endgroup$ Jan 28, 2020 at 7:23
  • $\begingroup$ Yes. I have looked at the message online. The answer I saw is that "It means your design matrix is not invertible". But then, I do not have clue on how to adapt the solution when using R vars package. $\endgroup$
    – William
    Jan 28, 2020 at 8:46
  • $\begingroup$ No package will help you if the problem lies in the data. You need to reconsider the variables you have; some of them form a linear combination equal to a constant. To solve the problem, you could get rid of the variable(s) causing that. $\endgroup$ Jan 28, 2020 at 9:47
  • $\begingroup$ @RichardHardy, my guess would be severe overfitting rather than multicollinearity here. $\endgroup$ Jan 28, 2020 at 12:13
  • $\begingroup$ @ChristophHanck, yes, that must be the case. I did not inspect the data and forgot to consider this possibility. $\endgroup$ Jan 28, 2020 at 12:24

1 Answer 1

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Your time series is too short to fit that many parameters. Recall that, in a VAR(p) model \begin{equation*} x_t = d + A_1 x_{t-1} + A_2 x_{t-2} + \dots + A_p x_{t-p} + \epsilon_t, \end{equation*} each parameter matrix $A_i$ will have dimension $k\times k$, where $k$ is the number of parameters. Estimation simply procedes by OLS to each equation of the VAR model. That means you will have $1+k\times p$ parameters per equation (assuming $d$ for the deterministic component is just a constant). In your case, $p=6$ and there are $k=8$ variables (although two of these appear to be identically zero and hence not very useful).

Hence, you fit 49 coefficients for each equation, but only appear to have $n=21$ observations. As is well-known, the $X'X$ matrix of the OLS estimator will not be invertible when $n$ is smaller than the number of regressors.

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  • $\begingroup$ I am getting a similar error message after running (VAR_reduced <- VAR(VAR_data_1, p = 1, type = "both")) summary(VAR_reduced) but with a condition number just above zero. I am only using 3 variables but have 135 observations, so I should not be overfitting. Any idea what may cause that? Maybe I should add that I only get the error message after summary $\endgroup$
    – ArOk
    Jul 24, 2020 at 14:17
  • $\begingroup$ Can you post a reproducible example, perhaps as a new question? $\endgroup$ Jul 25, 2020 at 7:07
  • $\begingroup$ I have but on stack overflow I assumed it would fit better there, stackoverflow.com/questions/63077895/… $\endgroup$
    – ArOk
    Jul 25, 2020 at 8:22

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