Robust Change Point Test for General Integer-Valued Time Series Models Based on Density Power Divergence

Abstract

In this study, we consider the problem of testing for a parameter change in general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family when the data are contaminated by outliers. In particular, we use a robust change point test based on density power divergence (DPD) as the objective function of the minimum density power divergence estimator (MDPDE). The results show that under regularity conditions, the limiting null distribution of the DPD-based test is a function of a Brownian bridge. Monte Carlo simulations are conducted to evaluate the performance of the proposed test and show that the test inherits the robust properties of the MDPDE and DPD. Lastly, we demonstrate the proposed test using a real data analysis of the return times of extreme events related to Goldman Sachs Group stock.

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

“…Moreover, additionally assuming Kim and Lee [ 37 ] showed that the CUSUM test statistics designed for detecting a change in have the limiting null distribution of the sup of a Brownian bridge. In practice, is often harnessed and an optimal can be selected through the method of Warwick [ 39 ] and Warwick and Jones [ 40 ]; see Remark 1 of Kim and Lee [ 36 ].…”

“…In this section, we apply to a real dataset, using the extreme events of the daily log-returns of GS stock from 2 July 2007 to 28 February 2020. Davis and Liu [ 11 ] and Kim and Lee [ 37 ] used the GS stock datasets with different periods, but their works were focused on parameter estimation and the retrospective change point test. For the task of online monitoring, we first calculated the hitting times, for which the log-returns of GS stock fall outside the 0.05 and 0.95 quantiles of the data, and generated the time series of counts , .…”

“…The MDPDE method has been successfully applied to various time series models, and in particular INGARCH models (Kim and Lee [ 35 ], Kim and Lee [ 36 ]). Recently, Lee and Lee [ 26 ] and Kim and Lee [ 37 ] considered the CUSUM tests based on score vectors for the MLE and MDPDE in exponential family distribution INGARCH models. See also Kang and Song [ 38 ].…”

Robust Estimation for Bivariate Poisson INGARCH Models

“…Among the robust estimation methods, we employ the minimum density power divergence estimator (MDPDE) approach that was originally proposed by Basu et al [ 22 ], because it is well known to consistently provide robust estimators in various situations. 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.…”

Robust Procedures for Estimating and Testing in the Framework of Divergence Measures

“…A real data analysis of the return times of extreme events of Goldman Sachs Group (GS) stock prices is also provided to illustrate the validity of the proposed test. These authors, see [24], considered the CUSUM tests based on score vectors for the MLE and MDPDE in exponential family distribution INGARCH models.…”