I conducted a research with 90 participants who were exposed to a film stimuli for 60 minutes and their physiological responses were measured continuously. I would like to test the causal relationship between this psychological response and a another continously measured visual feature of the stimuli. Physiology was measured 15 times per second, the visual feature was measured 1 time per second.

I think that I need to use a cross-correlation and I found a function for it in SPSS (I am only able to work with SPSS and I have no background in mathematics). As I am complete beginner in time-series analysis, I would like to know:

- if cross-correlation is the correct statistic here or whether I should use some other type of model?
- if I need to consider anything during the data preparation

(detrending is often mentioned in the literature, but I don't know

how to do that in SPSS or if I need it at all)? - if there is a book with a gentle introduction to this topic?

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#### Best Answer

You would likely be looking to calculate the residual autocorrelation function (RACF), also called residual cross-correlation function, which is the autocorrelation function on the residuals of fitted models for two different time series (fitted using ARMA models, auto-regressive moving average models). The calculation will yield a plot that shows if there is a causality between the two inputs, X and Y, and at what lags it is significant.

In order to fit the ARMA models properly, there are some assumptions made. The model should be stationary, so you may need to use a differenced ARMA model in fitting (see ARIMA). There are also the usual assumptions in fitting an ARMA model, such as normality of data, iid, constant variance. You should check these in your data before proceeding; there are some transformations you can do to your data to help make them more normal if required (such as Box-Cox).

In terms of a textbook, I took a course with this professor and found the book to be fairly helpful. The link is no longer working but you can likely find another copy somewhere. http://www.systems.uwaterloo.ca/Faculty/Hipel/Time%20Series%20Book.htm

Hope that helps. I am afraid I don't work in SPSS so I can't help you there (I work in R myself). If you can find a way to fit ARMA models in SPSS and get the residuals, you should be able to use the cross-correlation function on the residuals for your statistic.

Best of luck!