I have multiple environmental time series variables (for example: temperature, dissolved oxygen, conductivity, depth) measured every few minutes for several months. The variables are measured at different intervals but I could create an interpolated data set such that all data are placed at the same times.
I want to be able to understand how these variables are related to each other. For example I would be interested in a question like:
Is an increase in depth correlated with a decrease in temperature?
The variables may change at the same time, but more likely there will be some lag time between a change in depth and a change in temperature. Plus I would like to look at many variables – not just 2.
I am not interested in cycles or trends within one time series – just how one may affect another.
I am not sure where to start – is this just a multiple regression? How do I take lag time into account? Could you suggest topics I could read about?
You should look to Box-Jenkins Transfer Function modeling. It was Chapter 11 in their book. http://books.google.com/books?id=jyrCqMBW_owC&printsec=frontcover&dq=box+jenkins+time+series&hl=en&sa=X&ei=sDO-U4aCC8WZyASIkoLoBg&ved=0CDYQ6AEwAQ#v=onepage&q=box%20jenkins%20time%20series&f=false
Here is a link that explains the differences between regression vs Transfer Function models. http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/24-regression-vs-box-jenkins
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