Robust estimation for general integer-valued time series models

Kim, Byungsoo; Lee, Sangyeol

doi:10.1007/s10463-019-00728-0

Cited by 18 publications

(31 citation statements)

References 30 publications

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“…Kim and Lee [ 22 ] showed that under the regularity conditions (A0) – (A9) stated below, the MDPDE is strongly consistent and asymptotically normal. Conditions (A10) and (A11) are imposed to derive the limiting null distribution of the DPD-based change point test in Section 2.2 .…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…Instead of (A6) , Kim and Lee [ 22 ] assumed

to prove Proposition 1. Note that this condition is satisfied directly if (A3) and (A6) hold.…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…Based on the above and (A4) , the conditions (A2) , (A5) , and (A7)–(A10) are all satisfied for INGARCH(1,1) models, as proven by Theorem 3 of Kang and Lee [ 15 ]. Kim and Lee [ 22 ] showed recently that the following Poisson and negative binomial INGARCH(1,1) models satisfy (A3) and (A4) . Furthermore, following the arguments presented in Section 3.2 of their study, (A6) holds for these models as well.…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…In addition to the above models, general integer-valued time series models also include nonlinear models, such as the integer-valued threshold GARCH (INTGARCH) model:

where

with

is compact, and l is a non-negative integer value. For more details, see Remark 3 in Kim and Lee [ 22 ].…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…For earlier works in the context of time series, see Lee and Song [ 18 ], Kim and Lee [ 19 ], Kang and Lee [ 20 ], and Kim and Lee [ 21 ], who deal with the MDPDE for GARCH models, multivariate times series, and (zero-inflated) Poisson AR models. Kim and Lee [ 22 ] demonstrated that the MDPDE for general integer-valued time series models has strong robust properties, with little loss in asymptotic efficiency relative to the CMLE. This motivates us to use the MDPDE to construct a robust change point test for general integer-valued time series models.…”

Section: Introductionmentioning

confidence: 99%

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

Kim

Lee

2020

Entropy

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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.

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Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…Instead of (A6) , Kim and Lee [ 22 ] assumed

to prove Proposition 1. Note that this condition is satisfied directly if (A3) and (A6) hold.…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%

“…In addition to the above models, general integer-valued time series models also include nonlinear models, such as the integer-valued threshold GARCH (INTGARCH) model:

where

with

is compact, and l is a non-negative integer value. For more details, see Remark 3 in Kim and Lee [ 22 ].…”

Section: Construction Of the Mdpde And Change Point Testmentioning

confidence: 99%