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If you have multivariate (ie n time series) and you want to predict one of these time series using data from every column, you could use a VAR model (Vector Autoregression).

  1. What I dont understand is why I havent seen VAR model with moving averages taken into account, like with univariate ARMA models. Do they exist or why dont they?

  2. What are the alternatives to this for predicting one time series, using data from n time series? See 1.2 in here https://www.analyticsvidhya.com/blog/2018/09/multivariate-time-series-guide-forecasting-modeling-python-codes/

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  • $\begingroup$ VARMA models have been known for a long time, but VAR have been more popular for their ease of estimation. Estimation of VARMA in high dimensions is quite prohibitive computationally. But see the bigtime package as mentioned here for a recent advance in that problem. $\endgroup$
    – Richard Hardy
    Commented Oct 11, 2020 at 18:26
  • $\begingroup$ You might also want to learn about empirical dynamic modeling—including simplex projection, S-maps, convergent cross-mapping, and related methods—which provide a very different approach to time series prediction from VAR. $\endgroup$
    – Alexis
    Commented Oct 11, 2020 at 18:36
  • $\begingroup$ @Alexis i will look into those but i was hoping for things more simple. Are there issues regarding using standard ml algorithm with the dependent variable lagged 1 time step into the future? $\endgroup$
    – Trajan
    Commented Oct 16, 2020 at 10:57
  • $\begingroup$ So you are looking for alternatives, but are not actually interested in alternatives? Can you clarify what the second part of your question is asking? $\endgroup$
    – Alexis
    Commented Oct 17, 2020 at 17:39

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I'm a bit late to this party but depending on what you're trying to do, an OLS with time series errors model, or Vector Error Correction Models (VECMs) could work as an alternative to VAR if you're dealing with multiple time series. Lush thing about VECMs is that it models the cointegration directly in its structure, so it's way less of a pain that some of the other methods!

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