# How to define Autocorrelated Copula?

I want to make a copula between two auto correlated timeseries.Since it would be better for the timeseries not to be auto correlated, was thinking about making ARIMA (Autoregressive Integrated Moving Average) series based on each of these timeseries and use the timeseries Residuals (which basically is the timeseries minus ARIMA part) as the input of my Copula model.

But now the model does not converge and the series are so changed that it is almost impossible to see some properties of the original ones in the new one. Does anyone has any other suggestions on:

1: how can I eliminate autocorrelation (Other than ARIMA)?

2: If ARIMA is the solution, how can we use the ARIMA residuals as the Copula input?

3: Should I consider Autocorrolation in the Copula model? (I know the answer is generally yes, but is there a way to modify it?)

• (1) In what sense does ARIMA "eliminate" autocorrelation? (2) How do you propose applying a copula to an entire stochastic process like a time series? Are you perhaps assuming some kind of strong stationarity? (This could raise serious problems of mathematical realizability--if you impose a particular distribution for all bivariate values of the process, how can you know whether there even exists such a process?) (3) What would it mean to "consider autocorrelation in the Copula model"? – whuber Feb 5 at 19:53
• Dear @Whuber I appreciate your comment since it makes the whole thing more clear to me. 1-2: By using ARIMA, I make an autoreggresive timeseries. by removing the ARIMA values from the original timeseries (Timeseris-ARIMA Values=Residuals) I ll get to stationarity in my timeseries. 3: since most of our data are usually autocorrelated; how one uses this data in Copula model? – Frankova T Feb 6 at 8:50