# Regression coefficient(s) when explanatory & response variables are time series

I have multiple VMs (Virtual Machines) on one physical server (hardware machine). I have CPU utilization information (every 5 minute) for all the virtual machines and the physical server. Now I want to understand how each VM is contributing to the overall load of the physical server. I am assuming that this is a time series problem. The CPU utilization of each VM as well the physical server are separate time series. One way to approach this problem is to apply linear regression considering CPU utilization of each VM as explanatory varaibles and CPU utilization of physical server as response variable.

  cpu_physical_server(t) = Function(cpu_vm_one(t) + cpu_vm_two(t) + cpu_vm_three(t) + .....)


As per my understanding, I can't directly apply regression modelling (lm() or glm()) as these are all time series (Link).

The question is how to calculate the regression coefficients when both explanatory and response variables are time series? What kind of correction(s) should I apply?

• ARIMAX models combine time series characteristics with regression. That is likely the kind of model you want.
– Paul
Aug 27 '17 at 13:15

## 1 Answer

You should also have a look at the Cross Validated forum on StackExchange a lot questions asked there are related to time series analysis.

What you are looking for seems like a "Dynamic Regression or "Intervention Analysis" https://www.otexts.org/fpp/9/1 (with examples in R)

An here https://onlinecourses.science.psu.edu/stat510/node/72 you will find a procedure which does an ordinary linear regression but investigates the autocorrelated errors caused by the time series structure of your data (also with an example in R)