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Assume we have two datasets $X$ and $Y$ and I want to evaluate the cross correlation between them. What are the effects of nonlinearity trends within each dataset? That is, are there any relations between the linear and nonlinear trends in each data on the cross correlation between them?

I understand that the linear and nonlinear properties are "inner" properties for the dataset and it has not a direct relationship with the cross correlation with other dataset. However, can we say anything about the linear correlation (or cross correlation) between two datasets based on their linear and nonlinear trends within each dataset?

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  • $\begingroup$ Probably nothing can be said other than we shouldn't be talking about the simple pearson correlation coefficient when you have two time series that may or may not have trends of any kind. Can you describe what you precisely mean about the term "trend". $\endgroup$
    – IrishStat
    Sep 6 '17 at 19:58
  • $\begingroup$ @IrishSta Does the curve properties (for example, tiny exponential, sinusoids like, sawtooth or a mix of all what mentioned ) of each signal has an effect on the cross correlation with another signal? $\endgroup$
    – hbak
    Sep 6 '17 at 20:06
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i would assume so BUT as to precisely what that would be might require some mathematics . In general the pearson (ordinary) cross-correlation coefficient is only interpretable under very strict requiremnents viz. each series by itself is gaussian. The impact of alternative scenarios can be evaluated by actually constructing alternative series. You might want to look at Finding correlations between financial time series.

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