Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets. (31st January 2022)

• Record Type: Journal Article
• Authors: Xu, Chen; Zhang, Ye
• Is Part Of: Inverse problems. Volume 38:Number 3(2022)
• Publication Date: 2022-01-31
• Subjects: time series -- memory parameter -- wavelets -- spectral density -- asymptotically consistent -- log-regression -- stochastic process; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac48ca
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The asymptotic theory for the memory-parameter estimator constructed from the log-regression with wavelets is incomplete for 1/ f processes that are not necessarily Gaussian or linear. Having a complete version of this theory is necessary because of the importance of non-Gaussian and non-linear long-memory models in describing financial time series. To bridge this gap, we prove that, under some mild assumptions, a newly designed memory estimator, named LRMW in this paper, is asymptotically consistent. The performances of LRMW in three simulated long-memory processes indicate the efficiency of this new estimator.