{"id":"https://openalex.org/G2310697778","display_name":"Bayesian Inference of Time Series of Counts and Related Nonlinear Models","description":"We would like to focus on the following two time-series topics: 1. There are many situations where a time series count of events can be collected over time. In this project, we aim to propose some useful models to describe time series of counts which can account for some characteristics such as discreteness, over-dispersion, asymmetry, and serial correlation. This study advances the Autoregressive Conditional Poisson (ACP) model in two ways: firstly, we extend the ACP model with a flexible distribution. The generalized Poisson (GP) distribution can accommodate both over-dispersion and under-dispersion. We will consider generalized autoregressive conditional GP models. Secondly, we extend the ACP model to capture more flexible asymmetric and nonlinear responses, via threshold nonlinear forms, e.g. structural change. We will also consider testing for model adequacy and model selection. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme will be employed for inference. In many situations, we may obtain big non-negative counts over time. The big count data set cannot be well interpreted by the Poisson distribution. The goal is to find a function ( )g x such that ( ) ( ( ))x yf x g f x= , where Y is a Poisson random variable. We will design a transformed ACP model to overcome this difficulty. 2. Li et al. (2013) extend the classical threshold models via the regime switching mechanism mimicking a climatological example. Li et al. (2013) propose a self-exciting Buffered threshold autoregressive (BAR) model since there is a buffer zone for the model to switch regimes. In this proposal, we develop a BAR heteroskedastic model that permits nonlinearity in the conditional mean and conditional variance. We will develop a simulation-based approach to sequential parameter learning and filtering for the proposed model which is based on the idea of Polson, Stroud, and M\u00fcller (2008) for the state-space models. This filtering method is advantageous to financial applications, for example, pair trading strategy. The proposed methods will be illustrated using both simulated and real examples.","funder_award_id":"MOST103-2118-M035-002-MY2","funder":{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","doi":"10.13039/501100004663"},"funded_outputs":["https://openalex.org/W2158774545","https://openalex.org/W2255141750","https://openalex.org/W2279922475","https://openalex.org/W2295404335","https://openalex.org/W2300443955","https://openalex.org/W2303437522","https://openalex.org/W2549113249","https://openalex.org/W2560551712","https://openalex.org/W2584732415","https://openalex.org/W2588391398"],"funded_outputs_count":10,"parent_awards":[],"sub_awards":[],"sub_awards_count":0,"amount":1915000.0,"currency":"TWD","amount_usd":63202.99,"amount_usd_basis":"annual_average","recipients":[],"recipient_countries":[],"recipient_regions":[],"research_scope":{"is_research":true,"basis":"funder_default","tier":1},"funding_type":"research","funder_scheme":"\u5b78\u8853\u88dc\u52a9","start_date":null,"end_date":null,"start_year":2014,"end_year":2016,"landing_page_url":"https://www.grb.gov.tw/search/planDetail?id=8322440","doi":null,"provenance":"grb_most_projects","lead_investigator":{"given_name":null,"family_name":"\u9673\u5a49\u6dd1","orcid":null,"role_start":null,"affiliation":{"name":"\u9022\u7532\u5927\u5b78\u7d71\u8a08\u5b78\u7cfb","country":null,"ids":null},"author":null,"institutions":[]},"co_lead_investigator":null,"investigators":null,"works_api_url":"https://api.openalex.org/works?filter=awards.id:G2310697778","primary_topic":null,"topics":null,"institution_awarded":[],"updated_date":"2026-11-05T03:01:09.000Z","created_date":"2026-07-13T04:25:35.000Z"}