Abstract
In view of the complexity and asymmetry of finite range multi-state integer-valued time series data, we propose a first-order random coefficient multinomial autoregressive model in this paper. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares (CLS) and weighted conditional least squares (WCLS) estimators of the model parameters are derived, and their asymptotic properties are established. In simulation studies, we compare these two methods with the conditional maximum likelihood (CML) method to verify the proposed procedure. A real example is applied to illustrate the advantages of our model.
Highlights
Integer-valued time series data are fairly common in practice
In order to describe this kind of data more effectively, Ref. [1] proposed a binomial thinning operator “◦” defined as: Academic Editors: Fukang Zhu and
The rest of the paper is organized as follows: In Section 2, we introduce the first order finite-range random coefficient multinomial autoregressive (F-RCMAR(1)) process, and investigate some basic properties
Summary
Integer-valued time series data are fairly common in practice. For example, the number of major global earthquakes per year; the number of road accidents in successive months; the number of births at hospital per month, etc. [15] extended the binomial AR(1) process to a multinomial autoregressive model, which can describe finite-range integer-valued data with three states. We attempt to extend the F-MAR(1) process to a case with random coefficients, where the fixed αi , β i and γi in Equation (2) are replaced by i.i.d. random variables αit , β it and γit This type of extension will lead to more complex model structure and more difficult derivation of relevant probabilistic and statistical properties. The rest of the paper is organized as follows: In Section 2, we introduce the first order finite-range random coefficient multinomial autoregressive (F-RCMAR(1)) process, and investigate some basic properties. We introduce a first order finite-range random coefficients multinomial autoregressive (F-RCMAR(1)) process, which is defined as the following recursive equation: Definition 1. {Corr ( Xit , Xi,t+k )}i=1,2; k=1,2,··· of F-RCMAR(1) process can be negative or positive for different parameter combinations, which means that model (3) can describe both positively correlated and negatively correlated data
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