Integrating clustering and sequential analysis for improving the spectral density estimation and dependency structure of time series

Abstract

Time series models (TSMs) are used to forecast events based on verified historical data that are widely applied to describe natural and social phenomena. The spectral density function (SDF) of the TSM has the benefit to determine trends, periodic patterns and behavior of observable events and is used in degree of memory (DOM) which is used to identify independent and dependent structures. Therefore, paying attention to the estimator of SDF (SDE) is the cornerstone and desired goal in the statistical properties of TSMs. This paper gives a novel perspective for improving the SDE then dependency structure of TSMs by integrating clustering and sequential analysis. The accuracy of the lag window estimator (LWE) and periodogram estimator (PE), which are commonly used as SDEs in practice, is examined both with and without integrating the new proposed technique in order to figure out the efficacy of the new technique. Several circumstances, including independent and dependent data structures, TSMs with long and short DOMs, different numbers of clusters, and different dataset sizes, are used to carry out the investigation. The main findings indicate that: (i) The SDEs (PE and LWE) perform better when combined with the new proposed technique than when used alone. (ii) Using the new technique in conjunction with the SDEs results in absolutely perfect estimators for independent processes. (iii) High efficiency estimators for short memory TSMs arise when the new proposed technique is combined with the SDEs in the dependent processes; however, high efficiency in long memory TSMs (LMTSMs) is not guaranteed. (iv) Using the new technique, the correlation estimator behavior between SDEs and frequencies improves significantly with increasing DOM values of LMTSMs. (v) By applying the new technique for LMTSMs, the DOM estimator provides results indicating significant dependence. This study demonstrates that there are other efficient ways to improve the estimator than estimate techniques.