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


No reference, but I guess the standard time-series way to do it is to use some kind of auto-regressive model (AR-model)

$$X_t = c + \sum_{i=1}^p \varphi_i X_{t-i}+ \varepsilon_t$$

You can find it in any textbook on time-seies analysis. The $\varphi_i$ are vectors of parameters which must be fitted, and the pre-chosen order $p$ determines the maximum lag time (further, $\varepsilon_t$ is a Gaussian error term).

The AR-model is simply a multivariate linear regression using the previous $p$ results as predictor and the current result as target. Obviously, you can extend this ansatz to any other multivariate statistic method. For instance, you can incorporate $x_i x_j$ to model interactions, use a neural network, etc.

As an alternative and easier method, you can also model only a single predictor given the instances of all predictors at $p$ previous times. This is more convenient since many methods in statistics consider a scalar output. Also, the interpretation is a bit easier. For example, in your mentioned case (depth-temperature) and for linear regression, you would model the temperature and then -- if there is some correlation -- find significant magnitude of the model parameters related to depth.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.