Updated on 2021/12/08

写真a

 
TAMAKI, Kenichiro
 
Affiliation
Faculty of Political Science and Economics, School of Political Science and Economics
Job title
Associate Professor

Concurrent Post

  • Faculty of Political Science and Economics   Graduate School of Economics

  • Faculty of Social Sciences   School of Social Sciences

Research Institute

  • 2021
    -
    2022

    データ科学センター   兼任センター員

Degree

  • Waseda University   Doctor of Science

Research Experience

  • 2008.04
    -
     

    Waseda University   Faculty of Political Science and Economics   Associate Professor

  • 2005.04
    -
    2008.03

    Waseda University   Faculty of Science and Engineering   Research Associate

Professional Memberships

  •  
     
     

    Mathematical Society of Japan

  •  
     
     

    Japanese Association of Financial Econometrics and Engineering

  •  
     
     

    Japan Statistical Society

  •  
     
     

    International Society for Mathematical Sciences

 

Research Areas

  • Statistical science

Research Interests

  • Statistical Finance, Time Series Analysis

Papers

  • Asymptotic Expansion for Term Structures of Defaultable Bonds with Non-Gaussian Dependent Innovations

    Masakazu Miura, Kenichiro Tamaki, Takayuki Shiohama

    Asia-Pacific Financial Markets   20 ( 4 ) 311 - 344  2013  [Refereed]

     View Summary

    In the context of credit risk, the term structure models that have been studied in the literature are typically models driven by Brownian motion or standard jump diffusions. These models provide coherent modeling that is straightforward to implement. To make these models more flexible, we develop a discrete-time approximation of a continuous-time Vasicek term structure analysis with non-Gaussian and dependent innovations. Higher-order asymptotic theory enables us to evaluate the term structures of defaultable bonds. Numerical examples show that the effects of non-Gaussianity and the dependency of both risk-free rate and default process strongly influence the evaluation of defaultable bonds. As an application, we estimate the parameters of our proposed models for the Japanese corporate credit default swap market. © 2013 Springer Science+Business Media New York.

    DOI

  • JACKKNIFED WHITTLE ESTIMATORS

    Masanobu Taniguchi, Kenichiro Tamaki, Thomas J. DiCiccio, Anna Clara Monti

    STATISTICA SINICA   22 ( 3 ) 1287 - 1304  2012.07  [Refereed]

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    The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

    DOI

  • Preliminary test estimation for spectra

    Yusuke Maeyama, Kenichiro Tamaki, Masanobu Taniguchi

    STATISTICS & PROBABILITY LETTERS   81 ( 11 ) 1580 - 1587  2011.11  [Refereed]

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    For a general non-Gaussian stationary linear process, quasi-maximum likelihood estimation of a subset of the parameters of the spectral density is considered when the complementary subset is suspected to be superfluous. A preliminary test quasi-maximum likelihood estimator (q-MLE) of parameters is introduced and, in the light of its mean square error, is compared with the restricted and unrestricted q-MLE. (C) 2011 Elsevier B.V. All rights reserved.

    DOI

  • Higher order asymptotic bond price valuation for interest rates with non-Gaussian dependent innovations

    Tetsuhiro Honda, Kenichiro Tamaki, Takayuki Shiohama

    FINANCE RESEARCH LETTERS   7 ( 1 ) 60 - 69  2010.03  [Refereed]

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    This paper considers the effect on zero-coupon bond price valuation when short rate model has non-Gaussian dependent innovations. Higher order asymptotic theory enables Lis to obtain the approximate bond price formula. Some numerical examples are presented, where the process of innovations follows particular model. These examples indicate non-Gaussianity and dependency of innovations have a great influence on zero-coupon bond price. (C) 2009 Elsevier Inc. All rights reserved.

    DOI

  • Second-order properties of locally stationary processes

    Kenichiro Tamaki

    JOURNAL OF TIME SERIES ANALYSIS   30 ( 1 ) 145 - 166  2009.01  [Refereed]

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    In this article, we investigate an optimal property of the maximum likelihood estimator of Gaussian locally stationary processes by the second-order approximation. In the case where the model is correctly specified, it is shown that appropriate modifications of the maximum likelihood estimator for Gaussian locally stationary processes is second-order asymptotically efficient. We also discuss second-order robustness properties.

    DOI

  • Generalized information criteria in model selection for locally stationary processes

    Junichi Hirukawa, Hiroko Solvang Kato, Kenichiro Tamaki, Masanobu Taniguchi

    Journal of the Japan Statistical Society   38 ( 1 ) 157 - 171  2008

  • The Bernstein-von Mises theorem for stationary processes

    Kenichiro Tamaki

    Journal of the Japan Statistical Society   38 ( 2 ) 311 - 323  2008

  • Higher order asymptotic option valuation for non-Gaussian dependent returns

    Kenichiro Tamaki, Masanobu Taniguchi

    JOURNAL OF STATISTICAL PLANNING AND INFERENCE   137 ( 3 ) 1043 - 1058  2007.03  [Refereed]

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    This paper discusses the option pricing problems using statistical series expansion for the price process of an underlying asset. We derive the Edgeworth expansion for the stock log return via extracting dynamics structure of time series. Using this result, we I investigate influences of the non-Gaussianity and the dependency of log return processes for option pricing. Numerical studies show some interesting features of them. (c) 2006 Elsevier B.V. All rights reserved.

    DOI

  • Second order optimality for estimators in time series regression models

    Kenichiro Tamaki

    JOURNAL OF MULTIVARIATE ANALYSIS   98 ( 3 ) 638 - 659  2007.03  [Refereed]

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    We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator (beta) over tilde proposed by Hannan I Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-371. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of (beta) over tilde. Then it is shown that the second order asymtotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that (beta) over tilde has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of (beta) over tilde Numerical studies are given to confirm the theoretical results. (c) 2006 Elsevier Inc. All rights reserved.

    DOI

  • Power properties of empirical likelihood for stationary processes

    Kenichiro Tamaki

    Scientiae Mathematicae Japonicae   66 ( 3 ) 359 - 369  2007

  • Second order asymptotic properties of a class of test statistics under the existence of nuisance parameters

    Kenichiro Tamaki

    Scientiae Mathematicae Japonicae   61 ( 1 ) 119 - 143  2005

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Books and Other Publications

  • Optimal Statistical Inference in Financial Engineering

    Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki

    Chapman & Hall/CRC  2008 ISBN: 1584885912

Research Projects

  • Generalized empirical likelihood for time series

    Project Year :

    2013.04
    -
    2017.03
     

     View Summary

    When we analyze data using time series models, there are many steps such as model selection, estimation of parameters, and diagnostic checking. Generally, since these steps are separately implemented, time series data analysis is complicated. Also, interpretation is difficult when the results of these steps are different. Therefore, we propose empirical likelihood methods that can compute these simultaneously, and elucidated that it has excellent properties especially in diagnostic checking. Simulation studies also showed that the proposed method performed equally or better than the usual method in many cases

  • Theory and Applications for Mathematical Methods in Statistical Science

    Project Year :

    2007
    -
    2010
     

     View Summary

    Mathematical models that describe random phenomena depending on past, present and future are called stochastic processes. In this research we established statistically optimal estimation theory for general stochastic processes, and applied the theoretical results to various fields, e.g., finance, economics, medical sciences, engineering and environment etc., yielding a lot of contributions. We performed the research with many foreign researchers as well as domestic ones, and developed young researchers.

  • 局外母数をもつ時系列回帰モデルのセミパラメトリックな高次漸近理論

    科学研究費助成事業(早稲田大学)  科学研究費助成事業(萌芽研究)

    Project Year :

    2005
    -
    2007
     

     View Summary

    セミパラメトリックな高次推定では、時系列回帰モデルにおいて回帰係数の推定に残差スペクトルの非母数的推定量に基づいたHannan推定量の高次のasymptoticsを明らかにした。結果として通常の高次セミパラメトリック推定では、関与の推定量の分布の高次項は非母数推定量のカーネル関数に依存するが、Hannan推定量は、2次までの近似項がカーネル関数に依存しないという結論を得た。これは、従来のこの分野の結果と本質的に異なり、Hannan推定量の特殊性を示している。
    非正則モデルの統計解析においては、定常過程のスペクトル密度関数が不連続点を持つ場合のスペクトルのダイナミクス母数と不連続周波点の推測を行った。この結果、不連続周波点の推定量のasymptoticsは従来のそれと異なり、また漸近有効性の面でも、最尤推定量が一般に漸近有効とはならないで、Bayes推定量が漸近有効となることが判明し、従来の推定論と大きく異なることが判明した。
    正規過程の共分散関数の推定において、従来は標本共分散を用いるが、標本共分散関数で縮小、拡大項をつけた推定量を提案し、このasymptoticsを明らかにした。従来の標本共分散と新しい推定量は、3次の漸近理論の意味で、差があり、この差を2乗誤差で評価した。自己回帰モデルなどでは、単位根に近いほど、新しい推定量が従来のを改善していることが判明した。
    その他、局所定常時系列の判別解析で、理論的結果を得、その応用でも種々の結果を得た。

  • Bayes approach to time series models

     View Summary

    First, we considered the second order power properties of empirical likelihood for stationary processes. Next, we investigated an optimal property of the maximum likelihood estimator of Gaussian locally stationary processes by the second order approximation. To elucidate the effect on zero-coupon bond price valuation when short rate model has non-Gaussian dependent innovations, we derived the approximate bond price formula using higher order asymptotic theory. Moreover we investigated asymptotic distribution of the change point test statistic based on the frequency domain empirical likelihood

Presentations

  • 時系列モデルに対する高次漸近理論

    日本数学会 

    Presentation date: 2008.03

  • Higher order asymptotic option valuation for non-Gaussian dependent returns

    4th World Congress of Bachelier Finance Society 

    Presentation date: 2006.08

  • Second order optimality for estimators in time series regression models

    25th European Meeting of Statisticians 

    Presentation date: 2005.07

Specific Research

  • 非線形モデルによる高次のオプション評価

    2006  

     View Summary

    私は本年度Whittle measureによる高次漸近理論の研究を行い、この研究成果を学会等で発表しました。時系列解析では、従属性をもつデータを扱うので、尤度が大変複雑になります。それ故、推定や検定において、Whittle likelihoodがよく用いられます。これは、対数正規尤度の近似となっており、真の尤度より計算が容易であるという利点があります。また、近年、正規定常過程に対して、Whittle measureのContiguityが示されました。本年度の研究では、正規定常過程に対して、Whittle measureにもとづく検定と正確なmeasureにもとづく検定の高次の性質を議論しました。まず、定常過程の正規性を仮定し、Whittle likelihoodより構成される検定統計量のクラスを考えます。次に、この検定統計量に対して、2次のEdgeworth展開を用いて、Whittle measureと真のmeasureの下でのLeCam's third lemma型の高次の漸布の変換公式を与えています。これにより、検定統計量のWhittle measureの下での検出力から真のmeasureの下での検出力が導き出せます。現在、著書では、時系列の最適推測に基づいた金融工学を発展させつつあります。また、時系列モデルに対するベイズ手法によるアプローチを考え、Whittle likelihoodにもとづく推定量の事後確率の漸近的な性質を研究しています。この研究では、長期記憶過程を含む定常過程において、Whittle measureを用いたBernstein-von Mises theoremを示すことを目標としています。さらに、Nonergodicなモデルに対する上記の定理を得ることも目標としています。

  • 非定常時系列に対する高次漸近理論

    2005  

     View Summary

    私は、本年度の特定課題研究助成費により、非定常時系列に対する高次漸近理論に関して研究し、この研究成果の学会等での発表を行った。数理統計学において、推定・検定問題は非常に古典的なテーマである。独立標本に対する議論はもとより、様々な時系列モデルに対して最適推測、最適検定、最適判別理論が構築されている。これらの最適性の議論は漸近理論であり、一般的に、最適な推定量や検定統計量は無数に構成できる。それゆえ、1次最適なものの中でより良いものを見つけるために、また、近似の精度を上げるために、高次漸近理論が発展してきた。母数の推定問題に関しては、独立標本、定常時系列モデルでは、漸近中央値不偏推定量になるように修正した最尤推定量が2次最適になることが知られている。しかしながら、実証分析の立場から、現実の多くのデータでは、定常性の仮定は制限的であると思われるので、非定常過程の研究は有用である。私は、局所定常過程という重要な非定常過程に対して、母数の高次の最適推測を構築するために最尤推定量の2次の性質を明らかにした。まず、最尤推定量の分布関数に対する2次までのエッジワース展開を与えた。これにより、一般的に、最尤推定量は漸近中央値不偏推定量ではないことを示し、漸近中央値不偏推定量になるようにバイアス修正した最尤推定量が2次最適となることを明らかにした。さらに、伝達関数が高次の項まで十分に近似できる場合において、初項の時変スペクトルのみに基づく最尤推定量が真の時変スペクトルに基づく最尤推定量と同等になるという高次の頑健性が成り立つ条件を導いた。また、局所定常過程では、スペクトルの構造が時間と共に滑らかに変化するので、最尤推定量の高次の性質が時変量に依存しない十分条件を明らかにし、非定常性の影響を議論した。上記は、母数型推定量に対しての最適性の議論であるが、現在、非母数型推定量の最適性に関しての研究を行っている。

 

Syllabus

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