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?
 A: It appears that each sequence has a set (equally spaced) of possibly auto-correlated historical values. To answer the question is the sequence expected to increase,decrease or remain the same is at the heart of time series modelling with Intervention Detection. For example each sequence may be described in two possible ways : 1) y(t) = y(t-1) + trend plus etc ARMA structure OR 2 ) y(t)= b0 + b1*t where t=1,2,3,..... . plus ARMA structure. Two possible ways of assessing trend ! Now in general in case (1) there could be multiple differencing operators or in case (2) there could be multiple trend break points . Now just to generalize one step further i.e. make less presumptive specifications about the model sample space, either 1) or 2) could possibly include one or more Level or Step Shifts which are not trend changes but intercept changes. Tons of software confuse i.e. fail to distinguish between trend changes and level changes. Not to make this more complex than it already seems to be, one might have changes in parameters or changes in error variance over time. Thus your problem is solved . Now all you have to is to find out how to implement this in some reasonable time frame. Be careful to challenge a presumed a model-based approach that doesn't verify the Gaussian Assumptions or doesn't adhere to strict tests of necessity and sufficiency of a proposed model. Whew ! This tires me out specifying what you have to do to correctly answer your questions.
