Abstract
Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressive model with a bivariate innovation, which follows the asymmetric Hermite distuibution with five parameters. An attractive advantage of the new model is that the dependence between series is achieved by innovative parts and the cross-dependence of the series. In addition, the time series of counts are modeled with excess zeros, low counts and low over-dispersion. Next, we established the stationarity and ergodicity of the new model and found its stochastic properties. We discuss the conditional maximum likelihood (CML) estimate and its asymptotic property. We assessed finite sample performances of estimators through a simulation study. Finally, we demonstrate the superiority of the proposed model by analyzing an artificial dataset and a real dataset.
Highlights
Much effort has recently been put into the study of integer-valued time series models, a particular class of which are known as univariate constant coefficient INAR(1) models [1]; see [2,3,4] for recent reviews on this topic
This paper considered a more flexible BHRCINAR(1) model for bivariate integervalued time series data
Model to the 2-dimensional case, and it can be regarded as a generalization of the BINAR(1)
Summary
Much effort has recently been put into the study of integer-valued time series models, a particular class of which are known as univariate constant coefficient INAR(1) models [1]; see [2,3,4] for recent reviews on this topic. The above models assumed that parameter αij is not affected by various environmental factors Based on this point, a new bivariate random coefficient INAR(1) model was proposed. Popović [20] proposed a bivariate INAR(1) model with random coefficients, but it ignores the cross-correlation of the process { Xt } and it assumes random coefficients follow a specified binomial distribution. E(αij )4 ≤ κ, where κ and κare finite positive constants; (ii) For any i 6= j, At−i is independent with At− j ; (iii) Let E( At ) = A, and the largest eigenvalue of non-negative matrix A is less than 1. The conditional expectation converges to unconditional expectation as k → ∞ by assuming that the largest eigenvalue of non-negative matrix A is less than 1
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