Parameter estimation for binary time series using partial likelihood

Abstract

A time series with binary response variable is called a binary time series. Binary time series can be modelled using the Autoregressive general model and nonlinear regression approach. Kedem & Fokianos introduced a binary time series model through the Autoregressive and logistic regression approach. The parameters of binary time series are estimated using the Partial Likelihood method. The Partial Likelihood method is performed by determining the Partial Likelihood function derived from the marginal probability density function (pdf) of Bernoulli distribution. However, in the process of parameter estimation using this method, the form of final function to obtain parameters is not in the closed form equation. To face this problem, Fisher scoring iterations are performed. The application of parameter estimation of the model uses the data about boat racing competition between the University of Cambridge and Oxford University from 1946 to 2011. Based on the data application, parameter estimation of the binary time series model using partial likelihood with different amounts of data resulting in a relatively same or no significant parameter estimator.