A hybrid-domain approach on modeling nonstationary time series with multiple time-varying deterministic components.

摘要

In this dissertation, motivated by research needs in homogenization of climate data time series, an innovative hybrid-domain approach is developed to model nonstationary time series with multiple time-varying deterministic components, such as periodicities, trend and shifts in mean. A frequency domain approach, i.e., the OGP test with data-adaptive grouping parameter, is firstly proposed to detect multiple periodicities under mixed spectra. The probability distribution of the test statistic for the OGP test is derived. Then the hybrid-domain approach, named as the HD algorithm, is proposed by integrating the OGP test together with a time domain approach, i.e., the PMFred method, through an iterative procedure analogue to the backfitting algorithm. The performance of the proposed OGP test and the HD algorithm are evaluated via Monte Carlo simulations, respectively. Their power are further illustrated through applications in climate data time series.