# Assessing if set of sequences increase or decrease

I have a set of sequences of numbers, each sequence is independent from each other. I'd like to know if, "in general", these sequences increase, decrease or remain the same.

What I have done so far is a fitted a linear model to each sequence, so that I can use the gradient to determine if the sequence is increasing or not.

I am then using a Wilcoxson U test to test if to compare if the positive gradients are as large as the negative ones (in absolute value, of course).

Is this a good solution to my problems? What are the threats of this solution? What would be a better one?

• Is each component of each sequence uncorrelated with each other? If not, this could be misleading, since you have autocorrelation in the responses. – Macro Jul 14 '11 at 20:47
• I don't know if they are correlated or not. As this comes from a time series, it might well be, but that is one of the things I wish to find out too! – rafalotufo Jul 14 '11 at 21:11
• What's wrong with taking the first difference and performing a test of location (like the t-test)? – shabbychef Jul 14 '11 at 23:26
• @shabbychef You are assuming the ARIMA filter which will convert an autocorreleated series to a white noise series. Unfortunately a first difference filter an inject structure see the Slutzky Effect en.wikipedia.org/wiki/Eugen_Slutsky which teaches us that one can create an autocorrelated series by differencing a white noise series. Assuming a filter,any filter can be quite dangerous. ARIMA model identification en.wikipedia.org/wiki/Box%E2%80%93Jenkins is the procedure to follow in order to yield an equation and an error process that is Gaussian. See my comments in my answer . – IrishStat Jul 15 '11 at 0:57