Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach
- PDF / 662,064 Bytes
- 38 Pages / 439.37 x 666.142 pts Page_size
- 36 Downloads / 146 Views
Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach Xinyang Wang1 · Dehui Wang2
· Kai Yang3
Received: 31 July 2019 / Accepted: 7 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper proposes a penalized maximum quasi-likelihood (PMQL) estimation that can solve the problem of order selection and parameter estimation regarding the pthorder 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. Keywords Integer-valued time series · Penalized maximum Quasi-likelihood · Oracle properties · Nonparametric estimation
1 Introduction In recent years, integer-valued time series data has attracted many attention because such data exists in many fields, such as finance, biology, medicine, etc. This kind of data
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00184020-00799-7) contains supplementary material, which is available to authorized users.
B
Dehui Wang [email protected]
1
School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China
2
Mathematics School of Jilin University, Changchun 130012, China
3
School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
123
X. Wang et al.
is discrete count data hence traditional time series models cannot properly describe it. This poses great difficulties in analyzing practical problem. To overcome this defect, Alzaid and Al-Osh (1990) and Du and Li (1991) proposed the p-order integer-valued autoregressive (INAR( p)) model based on the binomial thinning operator (Steutal and Van Harn 1979). Since then, a great number of articles about integer-valued autoregressive time series models based on different thinning operators have arisen in the literature, see Weiß (2008) for a review. Besides the modeling idea of the INAR( p) model, Ferland et al. (2006) and Fokianos et al. (2009) pointed out that the latent process can also be used to describe the integer-valued time series data. Based on this idea, they proposed the p-order integer-valued autoregressive conditional heteroskedasticity (INARCH( p)) model. Since the INARCH( p) model can well describe the over-dispersed characteristics of the Poisson distribution, it is also commonly used in practice to fit integer-valued time series data. Fokianos 20
Data Loading...
