Robust Estimation for Bivariate Poisson INGARCH Models

Byungsoo Kim,Sangyeol Lee,Dongwon Kim

doi:10.3390/e23030367

Abstract

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

Highlights

Andreassen [18] later verified the consistency of the conditional maximum likelihood estimator (CMLE) and Lee et al [19] studied the asymptotic normality of the CMLE and developed the CMLE- and residual-based change point tests
Basu et al [22] showed the consistency and asymptotic normality of the minimum density power divergence estimator (MDPDE) and demonstrated that the estimator is robust against outliers, but it still retains high efficiency when the true distribution belongs to a parametric family
\ defined by that minimizes the trace of the estimated asymptotic mean squared error (AMSE)

Summary

Introduction

Andreassen [18] later verified the consistency of the conditional maximum likelihood estimator (CMLE) and Lee et al [19] studied the asymptotic normality of the CMLE and developed the CMLE- and residual-based change point tests This model has the drawback that it can only accommodate positive correlation between two time series of counts. For previous works in the context of time series of counts, see Kang and Lee [23], Kim and Lee [24,25], Diop and Kengne [26], Kim and Lee [27], and Lee and Kim [28], who studied the MDPDE for Poisson AR models, zero-inflated Poisson AR models, one-parameter exponential family AR models, and change point tests For another robust estimation approach in INGARCH models, see Xiong and Zhu [29] and Li et al [30], who studied Mallows’ quasi-likelihood method.

MDPDE for Bivariate Poisson Ingarch Models

Asymptotic Properties of the MDPDE

Simulation

Illustrative Examples

Concluding Remarks