This analysis estimates cross correlation between temperature deviations and CO2 levels, suggesting a methodological focus on white noise properties.
The purpose of this paper is discussing the estimation of cross correlation function between two time series, for instance, the monthly mean temperature deviations and monthly average CO2 levels. In order to tell if a cross correlation estimate is significantly different from zero, it should note that at least one of the series must be white noise. The method of prewhitening a time series must be very important for the cross correlation analysis. We consider the prewhitening method and discuss if there were truly a lead-lag-relationship between the real series.
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Minoru TANAKA (2019) studied this question.
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