Nonparametric Modeling and Break-Point Detection for Time Series of Counts

• Activity Number: 553
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Qi Gao* and Thomas C.M. Lee and Chun Yip Yau
• Companies: UC Davis and UC Davis and Chinese University of Hong Kong
• Keywords: genetic algorithm ; minimum description length ; time series of counts ; break point detection ; radial basis ; GARMA

Abstract

Time series of counts (e.g. the number of photons emitted by astronomical objects) arise in a wide range of scientific research such as astrophysics, epidemiology and social sciences. Moreover, structural breaks are commonly observed in such data (e.g. sudden increase in photon counts due to gamma ray bursts). In this project, we use Poisson Generalized Autoregressive Moving Average (GARMA) models to fit these data and radial basis expansions are used to enhance flexibility, stability and accuracy. A genetic algorithm is used to find the possible breaks and the best fitting model based on the minimum description length principle. The empirical performance of the proposed methodology is illustrated via a simulation study and a practical analysis of the bursts in the BATSE gamma ray data. Lastly, we prove the consistency of the maximum likelihood estimators of the parameters in the model under some regularity conditions.