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I am currently investigating the relationship between S&P 500 Spot and Future prices. Thes series contains daily closing prices of the past 4 years. Checking the residuals via a regression of the form Spot ~ Futures, tests show evidence of stationarity. Also the Johansen-Procedure confirms at least one cointegration relationship. I now constructed a VECM but i discover that when i include too many lags (above 4 lags) the ECT (error-correction-term) becomes insignificant. So the VECM essentially becomes a VAR. I also fitted a VAR to the data which yields a higher R^2 than the VECM. Tests for causality via the VAR are strongly significant for both so one cannot conclude that only one causes the other (which means that both are endogenous, am i correct?).

So my questions are:

  1. Do you have any idea why the ECT is becoming more and more insignificant the more lags i include (after 3 lags it becomes insignificant when i choose 2OLS as estimation method and after 5 when using ML)?

  2. Shall i then prefer the VAR over the VECM, even though i am interested in the long-run relationship (but which becomes insignificant when including more than 5 lags)?

Any help here is highly appreciated. I also hope that my request is not too trivial. I am not that experienced in the field of time series analytics.

Thanks for your support!

user14731396
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1 Answers1

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  1. Generally, including more lags tend to reduce the predictability since the statistically significant difference found in the error term is captured and diluted across multiple lag variables. The intuition behind this phenomenon is that markets have short-term memory and weigh shocks that happen a short time in the past more than shocks that happen in a long time into the past. I believe there are a few functions in your stats software that helps automatically select the optimal number of lags to be included in the VAR/VECM model based on information criterion.

  2. Since you note that Johansen-Procedure already confirms at least one cointegration relationship, there is no reason to discard your VECM model. Your VECM model would not work at 5 lags, but there is a number of lags that could have worked.

For further reading, you may refer to some other questions people ask about cointegration.

Help understanding how the cointegration equation for VECM models are derived

David LE
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  • Hi David, thank you very much for your reply. I would have one additional question cnoncerning 1. Correct me if i am wrong, but when i understand you correctly this means that the additional lags are essentially "sucking up" the informational content of the ECT. Is this correct? But since the ECT reflects the long-run relationship wouldn't this mean then that this additional lags which are first differences of further past periods (so representing short-run relationship) are now substituting the informational content of the long-rung relationship reflected in the ECT? – user14731396 May 16 '21 at 23:04
  • @user14731396 I don't know how to answer your second part of the question. I'll admit I got a little confused on that question. Regarding your 1st question, I assume you have corrected for residual autocorrelation in order to do any estimation in a VAR and you estimate the cointegrating rank. After this case, if you dont apply enough lags, you can introduce size distortion in your test results. If you apply too many lags, you will lose too much power to obtain correct estimates. So yes, additional lags do "suck up" more information from ECT, at a cost of lower power for each lag. – David LE May 17 '21 at 09:27
  • Thanks again for the feedback David. I also did a test on serial correlation of the VAR errors (serial.test) and no matter how many lags i include i always get the result of serial correlation i.e. a very low p-value for the test. Do you know why this could be the case. I thought that if i i include a sufficient amount of lags this serial correlation should disappear. – user14731396 May 17 '21 at 18:19
  • @user14731396 Sorry for the late reply. Ideally, there shouldn't be any serial correlation in VAR or VECM errors (final outcome). You should correct for serial correlation before your do VAR or VECM analysis. Are you sure you've selected the correct test (level, trend) for your VECM models, or have you seasonally adjusted your original data? Here is an [example](https://towardsdatascience.com/vector-autoregressions-vector-error-correction-multivariate-model-a69daf6ab618) of the workflow – David LE May 19 '21 at 01:40