Pearson correlation is an indication of linear relationship between two variables, and cross correlation is lag lead between variables. During Pearson correlation normalize data is important, also influences the result. Is normalize (standardize) data is necessary change the value during cross-correlation?
It might help:
https://www.researchgate.net/post/Do_we_need_to_standardize_variables_with_different_scales_before_doing_correlation_analysis
It is true that Pearson correlation coefficient gives the degree of the linear relationship between two variables when the two variables are interdependent and the cross correlation is lag lead between the variables.
However, for Pearson correlation coefficient, it is not necessary that the data are to be normalized.
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