I am trying to forecast a time series based on other monthly time series variables.

The variables are:

  1. endog -> number of users;
  2. exog -> marketing campaigns(in euros), Number of Updates, number of partners, Google Search views and Release(binary).

I found that the VAR model is a good approach to do that. However, one of the variables is a binary variable. Not sure about the impact of this variable on the model.

In order to avoid non stationary variables, the transformation for all the time series variables (except the binary) is just the difference of the variable on time T with the variable on T-1. is that Ok?

Finally. In order to interprete the result of the VAR I am using the IRF, however, the interpretation is not clear for me.


Any suggestion on the steps that I took?

  • $\begingroup$ What do you think about the answer? Is everything clear, or should I elaborate on anything? $\endgroup$ Aug 17, 2017 at 18:51
  • $\begingroup$ Thank you for the answer. One thing. The dependent variable is continues, three of the independent variables are binary; so, the logit model wouldn't work in that case. However, the answer is very clear and the info I found in the book helped me to continue in the model construction Regads $\endgroup$ Aug 21, 2017 at 11:34
  • $\begingroup$ The logit model would be applied for the binary variables, while a regression would be applied on the continuous variable, so as a system it would be a mix of logit and linear models. $\endgroup$ Aug 21, 2017 at 11:37
  • $\begingroup$ Great, welcome to Cross Validated then :) $\endgroup$ Aug 21, 2017 at 11:41

1 Answer 1


Using a linear regression (and each equation of a VAR model is a linear regression) is not a crime when the dependent variable is binary, especially if this variable is not of direct interest but rather just is a feature that happens to be useful for forecasting another variable. Yes, the domain of the fitted values is not the same as the domain of the dependent variable (real-valued vs. binary), but this does not mean a linear regression cannot be useful here. Perhaps this is also the case in your application.

But a neater approach could be to substitute the VAR equation for the binary variable by a corresponding logit equation that would give you fitted values between $0$ and $1$ that could be rounded to binary. However, such a model (a number of regular VAR equations and one logit equation) would require a more complicated estimation method (equation-by-equation OLS would no longer be an option). If you are comfortable with that, you could give it a try.

Regarding the IRFs, what is unclear to you? Have you tried following the presentation of IRFs in a lecture note or a textbook (e.g. Lütkepohl "New Introduction to Multiple Time Series Analysis", 2005, Section 2.3.2 "Impulse Response Analysis")? Where did you get stuck?


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