Determining statistical significance on exponential variables and timeseries I am attempting to determine statistical significance of various customer programs for farmers use of sustainable products. Farm sales of sustainable products follows roughly an exponential curve, where many people purchase little but a few purchase a lot. The customer programs tend to target the larger purchasing customers regardless of what type of crop or sustainable products they purchase. The programs run on year long intervals.
I am probably making this problem a lot harder than it needs to be, but I am thinking:
1). The problem is fundamentally being done on a time series, thus needs to be regression or needs the creation of an equivalent sample set during year 0 then tested against the following year. I could use a K-NN approach to make a similar sample during year 0 then test against it for difference of sustainable products based on enrollment the following year? Not sure what test given the distribution (2).
2). The distribution being looked at is exponential, thus standard statistical tests are no good by itself and standard non-parametric solutions don't seem right either. I am guessing the best solution would be to change the problem into a gaussian question by looking at the problem more as a regression problem and looking for an increased slope (or exponent) in this situation? I am guessing a K-NN sampling would still be needed, given the potential variance of high purchasing customers?
Any insight would be greatly appreciated!

Your basic question is how to deal with an exponentially distributed time series in a regression. The generalized linear model provides a powerful and flexible regression framework. For an exponentially distributed outcome, a GLM with a Gamma family, that is an inverse link and a ^2 variance, meets the probabilistic requirement of an exponentially distributed RV. Since this RV is in the exponential family, this is a maximum likelihood procedure, in much the same way that linear regression is the MLE for a normally distributed response.
Further considerations for the time-series nature of the data can thus be handled in the same way that one would handle them in a linear regression model, either by adjusting for exogenous time, lagged response or covariates, or including a covariance structure in a GLMM - a generalized linear mixed model.
Clustering algorithms, like KNN, don't seem to have anything to do with the problem.
