Tools for model selection for mean-nonstationary time series

Yang, Shuhan (2023) Tools for model selection for mean-nonstationary time series. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis studies the problem of detecting multiple change-points of the process with a piecewise-constant signal plus dependent noise, and analysing lead-lag relationships between nonstationary time series. Motivated by the demand of long-run variance (LRV) in extending the application of existing change-point detection (CPD) approaches proposed for independent time series, the first part of the thesis introduces novel wavelet-based consistent LRV estimators to quantify the level of noise in mean nonstationary processes. In our proposed estimators, a particular blend of wavelets and well-suited thresholds make our methods lie somewhere in between the two broad classes of LRV estimators: residualand difference-based estimators. Specifically, they bypass the difficulty in the preestimation of signals and can be robust to potential outliers that largely impact the performance many difference-based estimators. Several asymptotic properties of our estimators are proved, and their performance are illustrated through comparative simulation studies. Secondly, we study the aspects of model selection for nonstationary time series with level change. In particular, we explore the possible extensions of the Narrowest-Over- Threshold (NOT) detection algorithm, hoping that it can show better performance for serially correlated data. Our attempts mainly consist of three parts and we provide more detailed discussion of the last two, including data-preprocessing and the modification of the strengthened Schwarz Information Criterion (sSIC) applied in NOT solution path algorithm. Many simulations are conducted to demonstrate the practicability of our ideas. Lastly, motivated by the dynamics of COVID-19 datasets, our interest shifts towards investigating lead-lag relationships between nonstationary time series. Relying the “scalespace” viewpoint employed in the SIgnificant ZERo crossings of derivatives (SiZer) map, we introduce an exploratory approach, Multi-scale Lead Lag Heatmap (MLLH), for providing an broad view of (possible) significant relations between two time series, which may serve as the first step for further lead-lag or causal analyses. Starting from simple examples, we develop and describe several heatmaps that display significant features of simulated bi-variate data over both locations and scales. Finally we assess the performance of MLLH on real-world COVID-19 data examples.

Item Type:	Thesis (PhD)
Additional Information:	© 2023 Shuhan Yang
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Supervisor:	Fryzlewicz, Piotr and Chen, Yining
URI:	http://etheses.lse.ac.uk/id/eprint/4630

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