The Statistical Property of the Wavelet-Based Estimator for Long-Memory Processes with Missing Data

Research Project

Project/Area Number	15H06525
Research Category	Grant-in-Aid for Research Activity Start-up
Allocation Type	Single-year Grants
Research Field	Economic statistics
Research Institution	Aomori Public College
Principal Investigator	NANAMIYA Kei 青森公立大学, 経営経済学部, 講師 (20755714)
Project Period (FY)	2015-08-28 – 2017-03-31
Project Status	Completed (Fiscal Year 2016)
Budget Amount *help	¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000) Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords	時系列解析 / 長期記憶過程 / 欠測値 / ウェーブレット解析 / 経済統計学 / 計量経済学
Outline of Final Research Achievements	We introduce the wavelet-based approximated maximum likelihood estimators for the parameters of the long-memory processes with missing data, and explore the statistical property of these estimators. In our study, by approximating the wavelet coefficients of the processes with missing data as white noise processes in each level and by removing the coefficients including missing data, we propose the wavelet-based approximated maximum likelihood estimators. We show that these estimators are not affected by missing data and have the same statistical property as the wavelet-based approximated maximum likelihood estimators for long-memory processes which are complete data.