The University of Tokyo · Mathematics
Professor Fumiya Akashi's research lab specializes in statistical inference for time series with non-elliptical and heavy-tailed distributions, focusing on robust and nonparametric methods under weak moment conditions. The lab develops advanced empirical likelihood and self-normalized techniques for change-point detection, M-estimation, and time-varying parameter models in the presence of long-range dependence or infinite variance. Key research directions include asymptotic theory for dependent and heavy-tailed data, semiparametric inference, and the construction of confidence regions without requiring knowledge of tail indices or dependence parameters. The lab emphasizes methodological innovation for real-world data with complex dependence and heavy-tailed behavior.
Figures are computed from collected data and may differ slightly.
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 empiri
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 gener
This article extends the self‐normalized subsampling method of Bai et al. (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 t
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with heavy-tails. This enable us to introduce a local approximation-based estimator which estimates consistently time-varying parameters of the model at hand. To develop a robust method, we also suggest a self-weighing scheme which is shown to recover the asymptotic
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 work 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 empiri
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