Presentations -
about 25-
Sequential criticality test for branching process with immigration
5. Keiji Nagai, Kohtaro Hitomi, Yoshihiko Nishiyama, and Junfan Tao
63rd ISI World Statistics Congress 2021 2021.7 International Statistical Institute
Event date： 2021.7
Language：English Presentation type：Oral presentation (general)
Venue：Online
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Local Asymptotic Optimality of Equivariant Sequential Estimation in Autoregressive Process
K. Nagai, K. Hitomi, Y. Nishiyama, and J. Tao
Kansai Keiryo Keizaigaku Kenkyukai 2024.1 Hiroshima Univ.
Event date： 2024.1
Language：English Presentation type：Oral presentation (general)
Venue：Hiroshima Country：Japan
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Unit root tests with initial values and a concise method for computing powers
金建偉， 人見 光太郎，永井 圭二，西山 慶彦，陶 俊帆
関西計量経済学研究会 2023.1 関西計量経済学研究会
Event date： 2023.1
Language：Japanese Presentation type：Oral presentation (general)
Venue：オンライン（大阪大学） Country：Japan
We consider a sequential sampling scheme of branching process. Observations are collected sequentially as time goes by. Statistics are evaluated when sufficient information is accumulated. For a sequentially observed branching processes with immigration, we use a stopping time based on the observed Fisher information. A sequential criticality test (SCT) is introduced for near criticality including sub-and-super-criticality. The joint density and Laplace transform of the test statistics and stopping time with initial values are obtained.
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Criticality tests for branching process with immigration
唐越之，永井 圭二
関西計量経済学研究会 2023.1 関西計量経済学研究会
Event date： 2023.1
Language：Japanese Presentation type：Oral presentation (general)
Venue：オンライン（大阪大学） Country：Japan
We consider a sequential sampling scheme of branching process. Observations are collected sequentially as time goes by. Statistics are evaluated when sufficient information is accumulated. For a sequentially observed branching processes with immigration, we use a stopping time based on the observed Fisher information. A sequential criticality test (SCT) is introduced for near criticality including sub-and-super-criticality. The joint density and Laplace transform of the test statistics and stopping time with initial values are obtained.
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Time-changed method in non-ergodic autoregressive process and branching process
Keiji Nagai, Yoshihiko Nishiyama, Kohtaro Hitomi, and Junfan Tao
日本経済学会秋季大会 2021.10 日本経済学会
Event date： 2021.10
Language：English Presentation type：Oral presentation (general)
Venue：大阪大学
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Sequential Test for the Criticality of Branching Processes
Keiji Nagai, Yoshihiko Nishiyama, Kohtaro Hitomi, and Junfan Tao
日本経済学会秋季大会 2021.10 日本経済学会
Event date： 2021.10
Language：English Presentation type：Oral presentation (general)
Venue：大阪大学
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Sequential Test for Unit Root in First Order Autoregressive Model
Keiji Nagai, Yoshihiko Nishiyama, Kohtaro Hitomi, and Junfan Tao
日本経済学会秋季大会 2021.10 日本経済学会
Event date： 2021.10
Language：English Presentation type：Oral presentation (general)
Venue：大阪大学
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Criticality test for branching processes with immigration
K. Nagai, K. Hitomi, Y. Nishiyama and J. Tao
統計関連学会連合大会 2021.9 統計関連学会連合，応用統計学会，日本計算機統計学会，日本計量生物学会，日本行動計量学会，日本統計学会，日本分類学会
Event date： 2021.9
Language：Japanese Presentation type：Oral presentation (general)
Venue：Online
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Sequential test for a unit root in monitoring a p-th order autoregressive process
10. Keiji Nagai, Yoshihiko Nishiyama, Kohtaro Hitomi, and Junfan Tao
日本経済学会春季大会 2021.5 日本経済学会
Event date： 2021.5
Language：English Presentation type：Oral presentation (general)
Venue：オンライン（関西学院大学）
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K. Nagai, K. Hitomi, Y. Nishiyama, and J. Tao
関西計量経済学研究会 関西計量経済学研究会
Event date： 2021.1
Language：Japanese Presentation type：Oral presentation (general)
Venue：オンライン（福岡大学）
We consider a sequential sampling scheme of branching process. Observations are collected sequentially as time goes by. Statistics are evaluated when sufficient information is accumulated. For a sequentially observed branching processes with immigration, we use a stopping time based on the observed Fisher information. A sequential criticality test (SCT) is introduced for near criticality including sub-and-super-criticality. The joint density and Laplace transform of the test statistics and stopping time with initial values are obtained.
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K. Nagai, K. Hitomi, Y. Nishiyama, and J. Tao
関西計量経済学研究会 関西計量経済学研究会
Event date： 2021.1
Language：Japanese Presentation type：Oral presentation (general)
Venue：オンライン（福岡大学）
When an unstable AR(p) process is observed sequentially, one wants to test the existence of unit root against stationary or local alternatives. Using stopping time based on observed Fisher information and sequential least square estimator (LSE), we propose three kinds of unit root tests; a Z test using the sequential LSE, a stopping time test using the stopping time as the test statistics, and a combination test with the sequential LSE and the Dickey-Fuller test.
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Sequential test for the criticality of branching processes
K. Nagai, K. Hitomi, Y. Nishiyama and J. Tao
統計関連学会連合大会 統計関連学会連合，応用統計学会，日本計算機統計学会，日本計量生物学会，日本行動計量学会，日本統計学会，日本分類学会
Event date： 2020.9
Language：Japanese Presentation type：Oral presentation (general)
Venue：Online
Due to great demand for statistical procedures to monitor the COVID19 pandemic, we consider sequential tests for the criticality of branching processes with and without immigration. Using stopping times based on the observed Fisher information, we propose three sequential tests, a locally most powerful test, a test whose rejection region is the right tail of the distribution of the stopping time, and a test combining the two tests. We derive asymptotic properties of three tests using Bessel process and Bessel bridge.
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K. Nagai, Y. Nishiyama, K. Hitomi, and J. Tao
統計関連学会連合大会 統計関連学会連合，応用統計学会，日本計算機統計学会，日本計量生物学会，日本行動計量学会，日本統計学会，日本分類学会
Event date： 2020.9
Language：English Presentation type：Oral presentation (general)
Venue：Online
We consider sequential testing problems on singularity in stochastic processes. Especially we focus on unit root test in autoregressive process and criticality test in branching process. Using diffusion approximation and time change, Bessel processes and Bessel bridges on squared Bessel play crucial roles to analyze the operating characteristics such as size, powers, moments of the sequential test statistics and the stopping times.
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K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao
Bernoulli-IMS One World Symposium Bernoulli and Institute of Mathematical Statistics
Event date： 2020.8
Language：English Presentation type：Oral presentation (general)
Venue：Online
We consider sequential testing problems on singularity in stochastic processes, especially, on a unit root in autoregressive process and the criticality in branching process. Using diffusion approximation and time change, we found that Bessel processes and Bessel bridges play crucial roles to analyze operating characteristics such as size, powers, moments of test statistics and stopping times.
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Operating characteristics of sequential unit root tests obtained from the Bessel bridges
K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao
Bernoulli-IMS One World Symposium Bernoulli and Institute of Mathematical Statistics
Event date： 2020.8
Language：English Presentation type：Oral presentation (general)
Venue：Online
Due to the demand for quick detection of emergencies in the financial market, such as the bubble and currency crises, we consider unit root tests under sequential sampling for a first-order autoregressive process. Using the stopping time based on the observed Fisher information introduced by Lai and Siegmund (1983), we propose three unit-root tests against local alternatives, including the explosive case. The first test is a Dickey-Fuller coefficient test with the sequential least square estimator. It becomes a Z-test by Lai and Siegmund’s result. As a test statistic, the second test sets a truncated stopping time with a predetermined bound computed from a quantile of the limiting distribution of the stopping time under the null. Combining the first and second tests like a Bonferroni test, we construct the third test with exact size. The limit of the Z-statistic can be represented by the Dambis-Dubins-Schwartz (DDS) Brownian motion and the limit of the stopping time can be characterized by a 3/2-dimensional Bessel process driven by the DDS Brownian motion under the null hypothesis. Using these facts and a time change, we derive the joint Laplace transform and joint density of the limits of the Z-statistic and the stopping time by the theory of the Bessel bridges in Pitman and Yor (1982). By applying Girsanov’s theorem under local alternatives, we obtain the joint Laplace transform and joint density under alternative hypothesis from the null’s results. Then, we can obtain the operating characteristics (OC’s) of the three tests such as sizes, powers, expected (truncated) stopping times, and some joint moments. We derive the joint Laplace transform since the joint densities are highly oscillatory and not appropriate to compute (joint) moments. We also find that the computations under local hypotheses are better than those under strongly stationary hypotheses when stable alternatives are true.
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Sequential unit root test for AR(p) processe
[9] K. Nagai, J. Tao, K. Hitomi, Y. Nishiyama, J. Tao [Invited]
Kansai Keiryo Keizaigaku Kenkyukai Kansai Keiryo Keizaigaku Kenkyukai
Event date： 2020.1
Language：Japanese Presentation type：Oral presentation (general)
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The relationship between Dickey=Fuller test and sequential unit root test
Keiji Nagai, Junfan Tao, Kotaro Hitomi, and Yoshihiko Nishiyama
Kansai Keiryo Keizaigaku Kenkyukai Kansai Keiryo Keizaigaku Kenkyukai
Event date： 2020.1
Language：Japanese Presentation type：Oral presentation (general)
Venue：Hitotsubashi University
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Sequential detection of the order of integration for pth-order autoregressive model
K. Nagai, Y. Nishiyama, K. Hitomi, J. Tao
2019 年度統計関連学会連合大会 日本統計学会他
Event date： 2019.9
Language：English Presentation type：Oral presentation (general)
Venue：滋賀大学
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The relationship between Dickey-Fuller test and Sequential unit root test for first-order autoregressive model
Japanese joint statistical meeting 2019 Japan Statistics Society etc.
Event date： 2019.9
Language：Japanese Presentation type：Oral presentation (general)
Venue：Shiga University
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K.Nagai
The 62nd ISI World Statistics Congress
Event date： 2019.8
Language：English Presentation type：Oral presentation (general)
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62nd ISI World Statistics Congress 2019
Event date： 2019.8
Language：English Presentation type：Oral presentation (general)
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Y. Nishiyama, Kohtaro Hitomi, Keiji Nagai [Invited]
Workshop on Recent Progress in Time Series in honour of Peter Robinson Graduate School of Economics and Management Tohoku University
Event date： 2019.5
Language：English Presentation type：Oral presentation (invited, special)
Venue：Tohoku University
Abstract We consider unit root test under monitoring sequential sample of autoregressive (AR) processes. We examine the property of the sequential autoregressive coefficient estimator evaluated at the stopping time based on the observed Fisher information, which was firstly introduced by Lai and Siegmund (1983) for fixed accuracy estimation. We propose three kinds of test: a t-type test (T test), a test using the distribution of the stopping time (ST test), and a Bonferroni test (BON test). We consider a local-to-unity hypothesis and adapt an approximation by Orstein-Uhlenbeck process. The sequential autoregressive coefficient estimator is found to be approximating to a Dambis, Dubins, and Schwarz (DDS) Brownian motion under unit root hypothesis and to a DDS Brownian motion with drift under a local-to-unity hypothesis. The asymptotic distribution of the stopping time is characterized by a Bessel process of dimension 3/2 under unit root hypothesis and also by a Bessel process of dimension 3/2 with drift under a local-to-unity hypothesis. Henceforth, T test turns out to be possessing local asymptotic normality (LAN). We implement Monte Carlo simulations and numerical computations to examine their small sample properties.
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Sequential estimation and unit root tests for autoregressive processes
Yoshihiko Nishiyama, Kohtaro Hitomi, Keiji Nagai, Junfan Tao [Invited]
Waseda International Symposium “Introduction of General Causality to Various Data & its Innovation of the Optimal Inference" Waseda Research Institute for Science & Engineering, Institute for Mathematical Science
Event date： 2018.10
Language：English Presentation type：Oral presentation (invited, special)
Venue：Waseda University, Nishi-Waseda Campus
Estimation and testing for autoregressive processes have a long history, where the literature mostly assume that off-line sampling data is available. Lai and Siegmund (1983) consider the case of online sampling, where they propose to stop sampling using the observed Fisher information and show that the OLS estimator of the AR coefficient is symptotically normally distributed for both stationary and nonstationary AR(1) processes. Motivated by the unit root testing problem, we consider the case of nearly nonstationary processes where we employ a unifying approach by diffusion approximation for both nonstationary and nearly nonstationary cases to examine the statistical properties. It allows us to scrutinize the properties of the stopping times we consider, which are shown to be characterized by Bessel processes of dimension 3/2. We also consider the stationary autoregressive processes and prove the asymptotic normality of the coefficient estimator and the stopping times.
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Sequential Estimation for Strongly Stationary AR(p) Process
Event date： 2018.9
Language：English Presentation type：Oral presentation (general)
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Sequential Estimation for Strongly Stationary AR(p) Process
Event date： 2018.9
Language：English Presentation type：Oral presentation (general)