Models for Time Series of Counts with Shape Constraints

Friday, February 23, 2018 - 9:10am - 9:50am
Lind 305
Richard Davis (Columbia University)
In recent years there has been growing interest in modeling time series of counts. Many of the formulated models for count time series are expressed via a pair of generalized state-space equations. In this set-up, the observation equation specifies the conditional distribution of the observation $Y_t$ at time $t$ given a {\it state-variable} $X_t$. For count time series, this conditional distribution is usually specified as coming from a known parametric family such as Poisson, negative binomial, etc. To relax this formal parametric framework, we introduce a shape constraint into the one-parameter exponential family. This essentially amounts to assuming that the {\it reference measure} is log-concave. In this fashion, we are able to extend the class of observation-driven models studied in Davis and Liu (2016). Under this formulation, there exists a stationary and ergodic solution to the state-space model. In this new modeling framework, we compute and maximize the likelihood function over both the parameters associated with the mean function and the reference measure subject to a concavity constraint. The estimator of the mean function and the conditional distribution are shown to be consistent and perform well compared to a full parametric model specification. The finite sample behavior of the estimators are studied via simulation and two empirical examples are provided to illustrate the methodology. (This talk is based on joint work with Jing Zhang.)