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I want to analyse temporal interactions of some time series by means of the Box-Jenkins approach to find out which time series are predictors of another one (with the help of prewhitening and computing cross correlations for some lags) and finally set up regression models. Besides I want to analyse the same time series in a vector autoregressive (VAR-) model approach.

When I looked at the plotted series in a first step I saw that some series are nearly constant over time. I have for example 140 time points and except for 10 time points the value is always 0. And the 10 values which are not 0 are nearly 0.

My question is: does it make sense to include such nearly constant time series in such multivariate time series models? If so how do I have to interpret the results?

Would be very happy if anyone can help me! Thank you very much.

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If it makes sense or not depends on the nature of the variables. I would just try to include them and test for Granger Causality and look at the their estimated coefficients and their t-values. If they are significant and it improves your forecast (if that is the goal) then it makes sense to include them, if they don't; remove them. Also how to interpret them depends on the nature of the variables, how does the value of the variables p lags ago affect your variable of interest?

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