Random coefficients integer-valued threshold autoregressive processes driven by logistic regression
- PDF / 1,902,098 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 57 Downloads / 160 Views
Random coefficients integer‑valued threshold autoregressive processes driven by logistic regression Kai Yang1 · Han Li2 · Dehui Wang3 · Chenhui Zhang3 Received: 16 March 2020 / Accepted: 21 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this article, we introduce a new random coefficients self-exciting threshold integer-valued autoregressive process. The autoregressive coefficients are driven by a logistic regression structure, so that the explanatory variables can be included. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators, as well as the asymptotic properties of the estimators, are discussed. The nonlinearity test of the model and existence test of explanatory variables are also addressed. As an illustration, we evaluate our estimates through a simulation study. Finally, we apply our method to the data sets of sexual offences in Ballina, New South Wales (NSW), Australia, with two covariates of temperature and drug offences. The result reveals that the proposed model fits the data sets well. Keywords Threshold integer-valued autoregressive models · Random coefficients models · Logistic regression · Explanatory variables
1 Introduction Researchers have placed much attention on time series of counts since they are frequently encountered in real world. The examples cover a broad range of studies including quality control (Li et al. 2019), epidemiology (Li et al. 2018; Pedeli et al. 2015), causal inference (Chen and Lee 2017), actuarial science (Shi and Wang 2014), economics (Brännäs and Quoreshi 2010), etc. As discussed in Chen and Lee (2017), the setups of many models describe the characteristics of integer-valued
* Han Li [email protected] 1
School of Mathematics and Statistics, Changchun University of Technology, Changchun, Jilin 130012, China
2
School of Science, Changchun University, Changchun, Jilin 130012, China
3
School of Mathematics, Jilin University, Changchun, Jilin 130012, China
13
Vol.:(0123456789)
K. Yang et al.
time series, in general, encompass two categories: one uses a generalized linear model (GLM) approach and the other employs a thinning approach. The well-known Poisson autoregressive model (Ferland et al. 2006; Fokianos et al. 2009) is a typical representative of the GLM approach. Examples of thinning approach include the integer-valued autoregressive (INAR) model (Al-Osh and Alzaid 1987), the integervalued moving average model (Brännäs and Quoreshi 2010) and the integer-valued bilinear model (Doukhan et al. 2006), among others. The thinning approach is based on some kinds of thinning operations. As discussed by Weiß (2008), the thinning operations are applied to random counts, and always lead to integer values results. This makes the thinning models very interpretable when modelling dependent discrete data. Weiß (2008) and Scotto et al. (2015) give detailed reviews of modelling and applications of integer-valued time series. For some
Data Loading...
