Date of Award

Summer 8-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics & Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Norou Diawara

Committee Member

Michael Pokojovy

Committee Member

Yet Nguyen

Committee Member

Khan Iftekharuddin

Abstract

Count time series arise across but are not limited to the environmental, biomedical, and social sciences, and they routinely violate the assumptions of classical models in two ways: the marginal rates are non-stationary, shifting at unknown structural breaks, and the dependence between series is non-linear, asymmetric, and itself time-varying. This dissertation develops a copula-based methodological framework for such data and applies it to global tropical cyclone (TC) activity. After reviewing the distributional and time-series foundations for count data the Poisson, negativebinomial, and Conway–Maxwell–Poisson families and their behaviour under serial dependence the dissertation contributes two linked frameworks. The first is a two-stage changepoint–copula framework: a penalized likelihood detector applied jointly to the d-variate Poisson series (with inter-series dependence carried by a latent Gaussian, equivalently a Gaussian copula with Poisson margins) isolates structural breaks, after which regime-specific bivariate copulas, fitted on randomized probability-integral-transformed (RPIT) pseudo-observations, characterize the dependence within each homogeneous period. Applied to annual TC counts across six ocean basins (1980–2024), it detects a break at the year 2000 and shows that cross-basin dependence reorganizes across it, with a marked increase in tail-dependent copula families in the recent regime. The second framework, the Causal Copula–Changepoint (CCC) model, lifts the pairwise analysis to a regime-specific directed acyclic graph (DAG), learned by a copula-based hill-climbing score on the same pseudo-observations, so that the difference between regime graphs localizes a causal rewiring of the network. We establish identifiability of edge direction under a single-chirality rotated-copula library and joint consistency of the two-stage estimator, and we validate both with a Monte-Carlo study. The CCC analysis confirms the year-2000 break and recovers a robust reorganization of the Western North Pacific in-links together with a stable, strengthening Eastern North Pacific–North Atlantic pathway. Together the two frameworks provide tools for detecting, estimating, and causally interpreting evolving dependence in non-stationary multivariate count time series.

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DOI

10.25777/ps92-1h86

ISBN

9798193214656

ORCID

0009-0000-7297-4953

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Available for download on Monday, April 12, 2027

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