Testing for Serial Dependence in Binomial Time Series Regression

• Activity Number: 515
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Government Statistics Section
• Author(s): Jieyi He*+ and William Dunsmuir
• Companies: and University of New South Wales
• Keywords: Parameter driven time series ; Binomial time series regression ; Nonstandarded score type tests ; Detecting autocorrelation

Abstract

This paper focuses on detection and estimation of serial dependence in binomial response time series by the parameter driven model in which, conditional on an unobserved stationary latent process, observations at each time follow a binomial distribution with probability of success related via a link function to predictor variables and the latent process. Maximum likelihood or Bayesian estimation requires computation of high dimensional integrals and simpler methods based on generalized linear models are inconsistent for binomial data. In this paper we show that use of standard generalized linear mixed modelling methods based on products of one-dimentional integrals provides easily implementable consistent and asymptotically normal estimators for the regression parameters. These asymptotic results are also required to derive the approximate distribution of score-type tests for serial dependence in the latent process. A key asymptotic result provides the finite sample approximation of the probability of concluding that there is no latent process when one is present. Simulations will also confirm these results and describe conditions for identifiability.