Multivariate Time Series I am trying to learn multivariate time series using R. I have two time series and I want to see if I could use one of those to predict the other one, and after that check if the model holds or there is no relationship between both variables.
Does anyone have an example that I could use to understand this concept?
Thank you and kind regards
 A: Disclaimer:
I am a wanna-be, an engineer, not a real statistician.  I'm too interested in things like production and dealing with business people, and I don't know enough theorems or have enough coursework.
My approach:
First, I assume about your data.  It is a sequence of numbers.  It is a vector, not a matrix.  (note to self: neo4j structure might make for an interesting heterogenous, possibly sparse, time series)  I'm going to assume that they are equal in size.
There is a quote that correlation is not causality.  They are bedmates, and a great place to explore.  If I compute the cross-correlation function, find the peak, and look at the change in time between concurrent, predictive, or consequent then I can get an idea of where they connect.
Notes:
Now I have seen, in my stock-price modeling, that there is some very-clever math going on in the noise.  You might want to pre-smooth your data.  You can get different results.  I have found fair results with AIC-informed smoothing spline on the intensity values, then performing the previous between them.  I was looking for some sort of coupled transactions.
Be sure to relate your approach to "physics".  Yes there are in fact social physics and business physics.  They are the causative laws of money and machinations of man.  If you are dealing with voodoo there is a guarantee that you solution fails first, and fails most completely.  The laws of physics can define the time-scale of relevance.  If the correlation is in a 5 or 20 day window, then to look outside of that is to confound the action that you are looking for with all previous actions.
Yes I am giving you some of my good tricks, and my hope is that they are useful to you. 
Examples: 
Others have laid out tutorials and examples that aren't bad introductions.    


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*NISt example (link)

*r-pro-bro tutorial (link)

*uChicago_Tsay (link)

*Monash_johnm (link)


Best of luck.
References:


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*http://ned.ipac.caltech.edu/level5/Sept01/Peterson2/Peter4.html
