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I have a set of monthly water quality data, and I want to use them in a few statistical analysis (such as finding distribution or using in copula models) which require random variables as input. I performed RUN TEST for randomness (runstest function in MATLAB) but the result showed that the data is not from a random data set. I tried removing seasonality from the data but it is still non random. Is there any way to transform or convert this data to a random data set so I acn use it in may analysis? Thank you

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    @HenningMakholm I don't want to kill all the signals, but I have been told that my data doesn't meet the requirement of the copula model's input (being a random variable). Also, somebody mentioned that I should do something about separating independent and time dependent parts. I but I don't know how to do it?2012-12-30

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You data $X$ are indexed by time $t$, so the runs test is a nonparametric test confirming autocorrelation in your data.

It may be there is a random component in your data, however, you may need to find an appropriate time-series model first. Also, removing seasonality may or may not have helped- it is important to know this is different from controlling for autocorrelation.

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    Without having looked at your data, my hunch is there is a strong likelihood there is a random component. And yes, there are a number of model selection techniques you can use to parameterize a sufficient time-series model, ARMA may be appropriate for what you're doing.2012-12-31