Prediction of periodically correlated processes by wavelet transform and multivariate methods with applications to climatological data

A Wavelet Characterization of Continuous‐Time Periodically Correlated Processes with Application to Simulation

“…Touati and Pesquet (2002) studied statistical properties of the wavelet packet decomposition for PC processes and determined their asymptotic distribution. Likewise, the advantages of wavelets for the prediction of PC processes rather than the classical method were shown in Ghanbarzadeh and Aminghafari (2015).Because of the periodicity of the mean and the autocovariance function of PC processes, to the best of our knowledge, there is no representation based on the wavelet basis on L 2 .R/ for them. The problem is the nonperiodicity of orthogonal wavelets on L 2 .R/.…”

“…Touati and Pesquet (2002) studied statistical properties of the wavelet packet decomposition for PC processes and determined their asymptotic distribution. Likewise, the advantages of wavelets for the prediction of PC processes rather than the classical method were shown in Ghanbarzadeh and Aminghafari (2015).…”