I want to find the cross-correlation of the three time series i.e., SST, SSS, and NINO4. Two of those (SST & SSS) have a strong seasonality and the rest one has an interannual cycle. How should I deal with those 3 to find the correlation?
I don't know well wavelets. A quick Google search lead me to a paper by A. Grinsted, J. C. Moore, S. Jevrejeva. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, European Geosciences Union
(EGU), 2004, 11 (5/6), pp.561-566. hal-00302394.
They refer to Torrence and Webster (1998). I would say that coherence corresponds roughly to correlation and partial coherence corresponds to partial correlation.
Cross wavelet shows the covariance between two time series at different time and frequency, the wavelet coherency shows the co movement of two series at different periods of time.. The dark arrow represents the phase of the wavelet as well as the direction of movement of the two series considered. The partial wavelet coherence shows the effect of an explanatory variable on the dependent variable given that the other variables ar kept constant.
Example : FDI :GDP | INFL
in other words, I want to effect of GDP on FDI keeping inflation constant.
You can read up this
Conriara et al 2018" estimating the Taylor rule in the time frequency domain"
Dear Md Masud-Ul-Alam ,
if you want to measure the interrelation between two signals , it is suggested to use WTC, which is the normalized version of the XWT. Not being normalized, XWT is not altogether a satisfactory method for coherency analysis.
Check out this paper of Maraun and Kurths (2004) on the pitfalls of XWT
https://www.researchgate.net/publication/29628361_Cross_wavelet_analysis_Significance_testing_and_pitfalls
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