I have taken a course based on the book "Introduction to Time Series and Forecasting" by Peter J. Brockwell and Richard A. Davis. I have learned about vector ARMA models, vector VAR models and Whittle's algorithm. I am interested in methods that employ exogenous variables in the univariate and multivariate cases. I can find mention of vector ARMAX models (with various names ARMAX/ARIMAX, XARMA/XARIMA, exogenous ARMA etc.) online and many packages that can model and predict these time series but I cannot find resource that explains the mathematics involved. Can anyone recommend a resource to learn how these models and the algorithms work?

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Helmut Lütkepohl "New Introduction to Multiple Time Series Analysis" 2005

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$\begingroup$ To add to the answer above, a simpler and possibly more intuitive way to start out on the journey that the OP described is to consider the "koyck distributed lag" model. Googling for that will bring up a lot of related links. $\endgroup$mlofton– mlofton2025-03-12 03:31:30 +00:00Commented Mar 12, 2025 at 3:31