Abstract/Details

Memory indicators and their incorporation into dynamic models


2009 2009

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Abstract (summary)

Data collected over time may exhibit some type of memory structure, such as a short or long term memory. Two commonly used indicators of memory are the Hurst exponent and the self-similarity index. We investigate the relationship between the Hurst exponent and the self-similarity index and show that the Hurst exponent is an estimator of the self-similarity index in some time series such as fractional Brownian motion. For time series with constant self-similarity index, we compare the statistical properties of various estimators of the self-similarity index via simulation for a range of nominal H-values between 0 and 1. We also employ windowing techniques to study the over-time behavior of the memory structure in a subset of the S&P500 series.

Further, we incorporate the memory indicators into dynamical models. In particular, and due to their popularity in terms of use, we look at two continuous-timed dynamical systems - the Log Ornstein-Uhlenbeck (LogOU) and the Cox-Ingersoll-Ross (CIR) models and investigate how to extend them by substituting the standard Brownian motion driver for a fractional driver in order to allow more flexibility in their memory structures. From the point of view of Young's integrals we confirm the well-definedness of the two new models by noticing that the smoothness of the CIR and fractional OU solutions is similar to the smoothness of their random drivers. We also explore the memory structures underlying these two updated models, and develop related results through analytical and numerical approaches. Finally, we discuss how to estimate the memory indicators and other model parameters simultaneously in the two model systems within a Bayesian framework.

Indexing (details)


Subject
Statistics
Classification
0463: Statistics
Identifier / keyword
Pure sciences; Hurst exponent; Memory indicators; Self-similarity index
Title
Memory indicators and their incorporation into dynamic models
Author
Li, Wen
Number of pages
123
Publication year
2009
Degree date
2009
School code
0097
Source
DAI-B 70/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109251944
Advisor
Carriquiry, Alicia; Kliemann, Wolfgang
Committee member
Carriquiry, Alicia; Kliemann, Wolfgang; Larsen, Michael; Liu, Peng; Wu, Huiqing; Yu, Cindy
University/institution
Iowa State University
Department
Statistics
University location
United States -- Iowa
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3360371
ProQuest document ID
304902507
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304902507
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