Updated on 2022/05/19


LIU, Yan
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Assistant Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering


  • 早稲田大学   博士(理学)

Research Experience

  • 2017.12

    Kyoto University   Graduate School of Informatics


    Waseda University Faculty of Science and Engineering



  • Minimax estimation for time series models

    Yan Liu, Masanobu Taniguchi

    METRON   79 ( 3 ) 353 - 359  2021.12


  • Shrinkage estimation for multivariate time series

    Yan Liu, Yoshiyuki Tanida, Masanobu Taniguchi

    Statistical Inference for Stochastic Processes   24 ( 3 ) 733 - 751  2021.10


  • Robust Linear Interpolation and Extrapolation of Stationary Time Series in L p

    Yan Liu, Yujie Xue, Masanobu Taniguchi

    Journal of Time Series Analysis   41 ( 2 ) 229 - 248  2020.03


  • Asymptotic Theory of Test Statistic for Sphericity of High-Dimensional Time Series

    Yan Liu, Yurie Tamura, Masanobu Taniguchi

    Journal of Time Series Analysis   39 ( 3 ) 402 - 416  2018.05  [Refereed]

     View Summary

    We consider the testing problem for the sphericity hypothesis regarding the covariance matrix based on high-dimensional time series, under the assumption that the sample size n and the dimension p satisfy Limn,p→∞ p/n = c ∈ (0, ∞). Recently, several studies on test statistics for sphericity of independent and identically distributed p-dimensional random variables have been carried out under the assumption that both n and p diverge to infinity. A test statistic for sphericity has been proved to be well behaved even when p&gt
    n. We investigate the test statistic under situations of high-dimensional time series. The asymptotic null distribution of the test statistic is shown to be standard normal distribution when the observations come from Gaussian stationary processes. In the simulation study, we illustrate the properties of the test statistic for several time series models. We apply the test to a problem of portfolio selection in our empirical study.


  • Change-point detection in autoregressive models with no moment assumptions

    Akashi, Fumiya, Dette, Holger, Liu, Yan

    Journal of Time Series Analysis   39 ( 5 ) 763 - 786  2018  [Refereed]

  • Robust parameter estimation for stationary processes by an exotic disparity from prediction problem

    Yan Liu

    STATISTICS & PROBABILITY LETTERS   129   120 - 130  2017.10  [Refereed]

     View Summary

    A new class of disparities from the point of view of prediction problem is proposed for minimum contrast estimation of spectral densities of stationary processes. We investigate asymptotic properties of the minimum contrast estimators based on the new disparities for stationary processes with both finite and infinite variance innovations. The relative efficiency and the robustness against randomly missing observations are shown in our numerical simulations. (C) 2017 Elsevier B.V. All rights reserved.


  • Discriminant and cluster analysis of possibly high-dimensional time series data by a class of disparities.

    Yan Liu, Hideaki Nagahata, Hirotaka Uchiyama, Masanobu Taniguchi

    Communications in Statistics - Simulation and Computation   46 ( 10 ) 8014 - 8027  2017  [Refereed]


  • Statistical inference for quantiles in the frequency domain

    Liu, Yan

    Statistical Infrence for Stochanstic Processes   20 ( 3 ) 369 - 386  2017  [Refereed]

  • Asymptotic theory of parameter estimation by a contrast function based on interpolation error

    Yoshihiro Suto, Yan Liu, Masanobu Taniguchi

    Statistical Inference for Stochastic Processes   19 ( 1 ) 93 - 110  2016.04  [Refereed]

     View Summary

    Interpolation is an important issue for a variety fields of statistics (e.g., missing data analysis). In time series analysis, the best interpolator for missing points problem has been investigated in several ways. In this paper, the asymptotics of a contrast function estimator defined by pseudo interpolation error for stationary process are investigated. We estimate parameters of the process by minimizing the pseudo interpolation error written in terms of a fitted parametric spectral density and the periodogram based on observed stretch. The estimator has the consistency and asymptotical normality. Although the criterion for the interpolation problem is known as the best in the sense of smallest mean square error for past and future extrapolation, it is shown that the estimator is asymptotically inefficient in general parameter estimation, which leads to an unexpected result.


  • Optimal portfolio of the Government Pension Investment Fund based on the systemic risk evaluated by a new asymmetric copula

    Liu, Yan

    Advances in Science, Technology and Environmentology   B13   21 - 38  2016  [Refereed]

  • An empirical likelihood approach for symmetric alpha-stable processes

    Fumiya Akashi, Yan Liu, Masanobu Taniguchi

    BERNOULLI   21 ( 4 ) 2093 - 2119  2015.11  [Refereed]

     View Summary

    Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of independent identically distributed random variables and second order stationary processes. In recent years, we observe heavy-tailed data in many fields. To model such data suitably, we consider symmetric scalar and multivariate alpha-stable linear processes generated by infinite variance innovation sequence. We use a Whittle likelihood type estimating function in the empirical likelihood ratio function and derive the asymptotic distribution of the empirical likelihood ratio statistic for alpha-stable linear processes. With the empirical likelihood statistic approach, the theory of estimation and testing for second order stationary processes is nicely extended to heavy-tailed data analyses, not straightforward, and applicable to a lot of financial statistical analyses.


  • Asymptotic Theory for Non-standard Estimating Function and Self-normalized Method in Time Series Analysis

    Liu, Yan

    Waseda University    2015

  • Variance stabilizing properties of Box-Cox transformation for dependent observations.

    Liu, Yan

    Advances in Science, Technology and Environmentology   B12   63 - 70  2015  [Refereed]

  • Asymptotics for M-estimators in time series

    Liu, Yan

    Advances in Science, Technology and Environmentology   B10   55 - 67  2014  [Refereed]

  • Asymptotic moments of symmetric self-normalized sums

    Liu, Yan

    Scientiae Mathematicae Japonicae   77 ( 1 ) 59 - 67  2013  [Refereed]

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Books and Other Publications

  • Empirical Likelihood and Quantile Methods for Time Series

    Liu, Yan, Akashi, Fumiya, Taniguchi, Masanobu( Part: Joint author)

    Springer  2018


  • 第35回 小川研究奨励賞

    2021   日本統計学会  

Research Projects

  • Theoretical development on statistical inference for local complex structure of temporal and spatial data

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :


  • Theoretical development of bootstrap and empirical likelihood method for method of spatio-temporal data

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :


    Liu Yan

     View Summary

    In time series analysis, statistical inference has been developed under regular conditions. It is well known that financial data do not have finite variance. In other words, the data do not satisfy the regular conditions. We applied the empirical likelihood method with the self-standardized periodogram to stable processes, known as stochastic processes with infinite variance. We also derived the asymptotic distributions and proposed a method for constructing the confidence region for pivotal quantities. As a wide class of time-series models including stable processes, we considered the prediction or interpolation error as a divergence between the true model and the parametric model, and developed the theoretical statistical inference for this method. In particular, the characteristics of the proposed statistical method were mathematically discussed from various viewpoints such as asymptotic effectiveness and robustness. These achievements have been summarized in a book and papers.

  • Research on the robust statistics applied to the time series models with infinite variance

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

    Project Year :


Specific Research

  • 欠損値を含む時系列データの新解析手法とその漸近理論の構築


     View Summary


  • 分位点回帰を用いた時系列解析とその応用に関する研究


     View Summary

    本研究は、分位点回帰を用いた時系列解析の理論に重きを置き、変化点問題についても考えた。特に、分位点回帰法に基づき、一般的なスペクトル構造の適切性を考えた。従来の手法と比較して、特殊な漸近分布を持つ驚くべき結果を得た。漸近正規性を回復する為、平滑化したピリオドグラムを利用した。それに対応して、通常の定常線形モデルに、非線型項を加えたsinusoid modelまで解析手法の理論的結果を拡張した。また、分位点検定論も展開し、数値シミュレーションを行った。本研究の成果は、Statistical inference for quantiles in frequency domainというタイトルの論文で投稿した。

  • 非有限分散時系列モデルとその解析手法の妥当性に関する統計的理論の新展開


     View Summary

    本研究では、非有限分散時系列モデルとその解析手法の妥当性について研究を進めた。時系列モデルの妥当性の問題の一つは、変化点問題である。通常、データを生成する一定のモデルは、パラメーターの変化に伴い、その構造が変化することがよくある。データ系列の中に変化点の有無を調べ、変化点が存在するとき、その変化点を見つけるのが問題である。ここでは、変化点の有無に関する検定論は、観測値が線形的構造を持つとし、その絶対誤差を最小にする検定法を提案した。Change point detection in autoregressive models with no moment assumptionsというタイトルの論文を投稿した。



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