氏名 | アカシ フミヤ ## 明石 郁哉 | 職名 | 次席研究員（研究院講師） | |

所属 | 理工学術院 （理工学術院総合研究所） | |||

## 論文

*Change point detection in autoregressive models with no moment assumptions*

Fumiya Akashi

Journal of Time Series Analysis査読有り39(5)p.763 - 7862018年05月-2018年05月

掲載種別：研究論文（学術雑誌）

概要：In this paper we consider the problem of detecting a change in the parameters of an autoregressive process where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is proposed and its asymptotic properties are studied. In contrast to other works on change‐point tests using empirical likelihood, we do not assume knowledge of the location of the change point. In particular, we prove that the maximizer of the empirical likelihood is a consistent estimator for the parameters of the autoregressive model in the case of no change point and derive the limiting distribution of the corresponding test statistic under the null hypothesis. We also establish consistency of the new test. A nice feature of the method is the fact that the resulting test is asymptotically distribution‐free and does not require an estimate of the long‐run variance. The asymptotic properties of the test are investigated by means of a small simulation study, which demonstrates good finite‐sample properties of the proposed method.

*Robust regression on stationary time series: A self‐normalized resampling approach*

Fumiya Akashi

Journal of Time Series Analysis査読有り招待有り39(3)p.417 - 4322018年04月-2018年04月

掲載種別：研究論文（学術雑誌）

概要：This article extends the self‐normalized subsampling method of Bai (2016) to the M‐estimation of linear regression models, where the covariate and the noise are stationary time series which may have long‐range dependence or heavy tails. The method yields an asymptotic confidence region for the unknown coefficients of the linear regression. The determination of these regions does not involve unknown parameters such as the intensity of the dependence or the heaviness of the distributional tail of the time series. Additional simulations can be found in a supplement. The computer codes are available from the authors.

*A new look at portmanteau tests*

Fumiya Akashi

Sankhya A査読有り80(1)p.121 - 1372018年02月-2018年02月

掲載種別：研究論文（学術雑誌）

概要：Portmanteau tests are some of the most commonly used statistical methods for model diagnostics. They can be applied in model checking either in the time series or in the regression context. The present paper proposes a portmanteau-type test, based on a sort of likelihood ratio statistic, useful to test general parametric hypotheses inherent to statistical models, which includes the classical portmanteau tests as special cases. Sufficient conditions for the statistic to be asymptotically chi-square distributed are elucidated in terms of the Fisher information matrix, and the results have very clear implications for the relationships between the parameter of interest and nuisance parameter. In addition, the power of the test is investigated when local alternative hypotheses are considered. Some interesting applications of the proposed test to various problems are illustrated, such as serial correlation tests where the proposed test is shown to be asymptotically equivalent to classical tests. Since portmanteau tests are widely used in many fields, it appears essential to elucidate the fundamental mechanism in a unified view.

*Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models*

Akashi, Fumiya

Statistical Inference for Stochastic Processes査読有り招待有り20(3)p.291 - 3132017年04月-2017年04月

掲載種別：研究論文（学術雑誌）ISSN：13870874

概要：This paper develops the generalized empirical likelihood (GEL) method for infinite variance ARMA models, and constructs a robust testing procedure for general linear hypotheses. In particular, we use the GEL method based on the least absolute deviations and self-weighting, and construct a natural class of statistics including the empirical likelihood and the continuous updating-generalized method of moments for infinite variance ARMA models. The self-weighted GEL test statistic is shown to converge to a (Formula presented.)-distribution, although the model may have infinite variance. Therefore, we can make inference without estimating any unknown quantity of the model such as the tail index or the density function of unobserved innovation processes. We also compare the finite sample performance of the proposed test with the Wald-type test by Pan et al. (Econom Theory 23:852–879, 2007) via some simulation experiments.

*An empirical likelihood approach for symmetric $\alpha$-stable processes*

Fumiya Akashi

Bernoulli査読有り21(4)p.2093 - 21192015年05月-2015年05月

掲載種別：研究論文（学術雑誌）

概要：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 multivariateα -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 forα -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.

*Empirical likelihood approach toward discriminant analysis for dynamics of stable processes*

Fumiya Akashi

Statistical Methodology査読有り19p.25 - 432014年06月-2014年06月

掲載種別：研究論文（学術雑誌）

概要：Discriminant analysis for time series models has been studied by many authors in these few decades, but many of them deal with second order stationary processes. In this paper, we introduce an empirical likelihood statistic based on a Whittle likelihood as a classification statistic, and consider problems of classifying an $\alpha$-stable linear process into one of two categories described by pivotal quantities $\theta_1$ and $\theta_2$ of time series models. It is shown that misclassification probabilities by the empirical likelihood criterion converge to 0 asymptotically without assuming that the true model is known. We also evaluate misclassification probabilities when $\theta_2$ is contiguous to $\theta_1$, and carry out simulation studies to make a comparison between goodness of the empirical likelihood classification statistic and that of an existing method. We observed that the empirical likelihood ratio discriminant statistic performs better than the existing method in some cases even if a family of score functions does not contain the true model. Since the stable processes do not have the finite second moment, this extension is not straightforward, and contains a lot of innovative aspects.

*An empirical likelihood approach for discriminant analysis of non-Gaussian vector stationary linear processes*

Fumiya Akashi

Scientiae Mathematicae Japonicae Online査読有りe-2013p.645 - 6602013年11月-2013年11月

掲載種別：研究論文（学術雑誌）

概要：In this paper, we apply the empirical likelihood approach to discriminant analysis of non-Gaussian vector stationary processes. We propose a classification statistic based on the empirical likelihood ratio function, and develop the discriminant procedure without assuming that the true spectral density matrix is known. Even if the true structure of the process is unknown, it is shown that the empirical likelihood classification criterion is consistent in the sense that the misclassification probabilities converge to 0 as sample size tends to infinity. A noteworthy point of the procedure is that the asymptotics of the empirical likelihood discrim-inant statistic for scalar processes are always independent of non-Gaussianity of the process under contiguous conditions.

## 外部研究資金

### 科学研究費採択状況

研究種別：

*自己加重経験尤度に基づく無限分散確率過程に対する非母数的・頑健な推測手法の構築*

2016年-0月-2020年-0月

配分額：￥3900000

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