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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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If you kill all of the signal first, then what on earth do you hope to learn from the eventual analysis? –  Henning Makholm Dec 30 '12 at 21:04
@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? –  Fred Dec 30 '12 at 21:18
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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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Thank you, Is it possible that my data does not contain any random component? in that case, does it mean that it cannot be used for my analysis? By time series model you mean that I should build a model like ARMA to separate random component? –  Fred Dec 30 '12 at 21:37
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. –  Bryce Dec 31 '12 at 0:20
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