# Multivariate Time Series Leading/Lagging Relations

Say I have an array of data of 10 time series $x_{i,t}$ at 1000 points in time. I wish to test the hypothesis that the first eight series are in some way a positive leading series of the other two.

So in other words (I think), the CCF between series $x_{1,t}$ or $x_{2,t}$ or $(x_{1,t}, x_{2,t})$ and $x_{j,t-k_j}$ for some group of $k_j$'s and all $2<j\le 10$ is positive so that when first eight series rise then in general so too do either/both my $(x_{1,t}, x_{2,t})$ and vice versa.

1. What type of model am I looking for?
2. Do I need to check for specifically a positive and specifically a leading series or can I just put the ten series into an algorithm of some kind that will determine which leads which and if so whether it's positive or negative?
3. How do I check specifically whether both of my lagging series are determined by all of my leading series or to what extent these relationships hold?
4. What's the best way to implement this in R?
• What about VAR model and the notion of Granger causality (but also impulse-response analysis)? – Richard Hardy Mar 24 '17 at 8:45
• Yes I have since discovered the VAR model and now plan on implementing it - I think this is what I was trying to describe above. I will also look into Granger causality and impulse response analysis. Thanks. – Denis Kelleher Mar 24 '17 at 13:01