Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator.

Sangyeol Lee,Dongwon Kim

doi:10.3390/e22111304

Abstract

In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.

Highlights

In this paper we consider the cumulative sum (CUSUM) monitoring procedure for detecting a parameter change in integer-valued generalized autoregressive heteroscedastic (INGARCH) models.Integer-valued time series is a core area in time series analysis that includes diverse disciplines in social, physical, engineering, and medical sciences
We do this because the minimum distance power divergence estimator (MDPDE) is well-known to be suitable for robust inference in various models, having a trade-off between efficiency and robustness controlled through the tuning parameters with little loss in asymptotic efficiency relative to the maximum likelihood estimator (MLE) (Riani, Atkinson, Corbellini and Perrotta [34])
This result indicates that Tncusum is improved when the MDPDE with α > 0 is used, which demonstrates the efficacy of the MDPDE in the monitoring process

Summary

Introduction

In this paper we consider the cumulative sum (CUSUM) monitoring procedure for detecting a parameter change in integer-valued generalized autoregressive heteroscedastic (INGARCH) models. In this work, taking the approach of Gombay and Serban [30] and Huh, Kim and Lee [31], we designate a robust monitoring process based on the minimum distance power divergence estimator (MDPDE) proposed by Basu, Harris, Hjort and Jones [33] We do this because the MDPDE is well-known to be suitable for robust inference in various models, having a trade-off between efficiency and robustness controlled through the tuning parameters with little loss in asymptotic efficiency relative to the maximum likelihood estimator (MLE) (Riani, Atkinson, Corbellini and Perrotta [34]). See Kang and Song [38] Using their results within the framework of Gombay and Serban [30] and Huh, Kim and Lee [31], we design an MDPDE-based monitoring process to detect a model parameter change in INGARCH models. The proof of the main theorem is provided in Appendix A

MDPDE for INGARCH Model

MDPDE-Based Monitoring Process

Real Data Analysis

Concluding Remarks