Wavelet Method in parameter estimation of stochastic processes: superiority of time-frequency localization

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400186
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Iwate University
• Principal Investigator: Kawasaki Shuji 岩手大学, 人文社会科学部, 准教授 (10282922)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 時間-周波数局在性

Outline of Final Research Achievements

Long-memory processes, known as a time series model that retains far past influences strongly, are observed in various fields of science and engineering. It is the so-called Hurst parameter that determines their probabilistic properties, so that its estimation is of fundamental importance. In evaluating the estimator, the asymptotic distribution of the estimator is essential. Often the distributions are not classical Gaussian distribution. In that case, the statistical evaluation will be complicated. However, the estimators in wavelet domain are able to turn the distribution to Gaussian, due to correlation decomposition of wavelet in time-frequency space. In this project, we have given the overall story of the covariance decay evaluation.

Free Research Field

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