Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations

Tonaki, Yozo; Kaino, Yusuke; Uchida, Masayuki

doi:10.1007/s11203-021-09249-1

Cited by 3 publications

(14 citation statements)

References 19 publications

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“…For nonergodic diffusion processes, see De Gregorio and Iacus (2008) and Iacus and Yoshida (2012). For ergodic diffusion processes, we can refer to Song and Lee (2009), Lee (2011), Negri and Nishiyama (2017), Song (2020), and Tonaki et al (2021a). De Gregorio and Iacus (2008) considered the detection of the parameter change in diffusion parameter and the estimation of the change point, and Iacus and Yoshida (2012) studied the estimation problem of the change point in diffusion parameter.…”

Section: Introductionmentioning

confidence: 99%

“…De Gregorio and Iacus (2008) considered the detection of the parameter change in diffusion parameter and the estimation of the change point, and Iacus and Yoshida (2012) studied the estimation problem of the change point in diffusion parameter. In contrast, Song and Lee (2009), Lee (2011) and Song (2020) considered the detection of the parameter change in diffusion parameter, and Negri and Nishiyama (2017) and Tonaki et al (2021a) considered the detection of the parameter change in diffusion and drift parameters. Specifically, Negri and Nishiyama (2017) proposed simultaneous test for changes in diffusion and drift parameters, and Tonaki et al (2021a) proposed adaptive tests for those changes.…”

Section: Introductionmentioning

confidence: 99%

“…When we consider the change point problem for ergodic diffusion processes, we first need to investigate whether there are any change points in the given data. Negri and Nishiyama (2017) considered the following hypothesis testing problem:

H_{0}^{θ} : θ = (α, β) does not change over 0 \leq t \leq T vs. H_{1}^{θ} : not H_{0}^{θ} .

In contrast, Tonaki et al (2021a) considered the adaptive tests for changes in diffusion and drift parameters. Specifically, consider the following steps.…”

Section: Introductionmentioning

confidence: 99%

“…With the adaptive detection method, when

H_{0}^{α}

is rejected, we can consider the estimation of the change point of the diffusion parameter

α

, and when

H_{0}^{α}

is not rejected and

H_{0}^{β}

is rejected, we can consider the estimation of the change point of the drift parameter

β

. It may be possible to estimate the change time using the maximum point of the CUSUM type test statistic proposed in Negri and Nishiyama (2017) and Tonaki et al (2021a), but these estimation methods have not been studied yet. Furthermore, we want to consider the change point estimation when the change is detected by some parameter change detection methods more generally.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 discusses the nuisance parameters of the proposed estimators. Section 4 presents the powers of tests proposed by Tonaki et al (2021a). In Sections 5 and 6, we give some examples and simulation studies.…”

Section: Introductionmentioning

confidence: 99%

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Estimation for change point of discretely observed ergodic diffusion processes

Tonaki

Kaino

Uchida

2022

Scandinavian J Statistics

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We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2021a) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion process models. When any change in the diffusion or drift parameter is detected by this or any other method, the next question to consider is where the change point is located. Therefore, we propose the method to estimate the change point of the parameter for two cases: the case where there is a change in the diffusion parameter, and the case where there is no change in the diffusion parameter but a change in the drift parameter. Furthermore, we present rates of convergence and distributional results of the change point estimators. Some examples and simulation results are also given. K E Y W O R D S adaptive tests, change point estimation, diffusion processes, discrete observations, test for parameter change 1

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

H_{0}^{θ} : θ = (α, β) does not change over 0 \leq t \leq T vs. H_{1}^{θ} : not H_{0}^{θ} .

In contrast, Tonaki et al (2021a) considered the adaptive tests for changes in diffusion and drift parameters. Specifically, consider the following steps.…”

Section: Introductionmentioning

confidence: 99%

“…With the adaptive detection method, when