Time series estimation by tracking parameter variation (Q2703258)

The measurements \(y_t=Y(\tau_t)\) are considered, where \(t=1,\dots,n\), \(\tau_t\) are unknown sampling times and \(Y(\tau)\) is believed to contain a cycle (not completely regular), so the spectrum of \(Y(\tau)\) should have a sharp peak at the true frequency \(f\). The problem is to estimate \(f\) and reconstruct the true time scale \(\tau_t=H(t)\). The authors use local ARMA techniques to reconstruct the cycle frequencies \(f=f_t\) locally and then build the scale \(H(t)\) basing on these local frequencies. Results of simulations and application to a geological data analysis are considered.