Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach

Abstract

This paper proposes a penalized maximum quasi-likelihood (PMQL) estimation that can solve the problem of order selection and parameter estimation regarding the pth-order integer-valued time series models. The PMQL estimation can effectively delete the insignificant orders in model. By contrast, the significant orders can be retained and their corresponding parameters are estimated, simultaneously. Moreover, the PMQL estimation possesses certain robustness hence its order shrinkage effectiveness is superior to the traditional penalized estimation method even if the data is contaminated. The theoretical properties of the PMQL estimator, including the consistency and oracle properties, are also investigated. Numerical simulation results show that our method is effective in a variety of situations. The Westgren’s data set is also analyzed to illustrate the practicability of the PMQL method.