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APPROXIMATING STATIONARY LONG MEMORY
PROCESSES BY AN AR MODEL WITH
APPLICATION TO FOREIGN EXCHANGE RATE
by
Shin-Huei Wang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful¯llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
August 2008
Copyright 2008 Shin-Huei Wang
Object Description
| Title | Approximating stationary long memory processes by an AR model with application to foreign exchange rate |
| Author | Wang, Shin-Huei |
| Author email | shin-huei.wang@uclouvain.be; modelhuei@hotmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Economics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2007-06-15 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-08-08 |
| Advisor (committee chair) | Hsiao, Cheng |
| Advisor (committee member) |
Hyungsik Roger Moon Jakasa Cvitatic |
| Abstract | This dissertation focuses on the AR approximation of long memory processes and its applications. The first chapter proposes an easy test for two stationary autoregressive fractionally integrated moving average (ARFIMA) processes being uncorrelated via AR approximations. We prove that an ARFIMA (p,d,q) process, \phi(L)(1-L)^{d}y_{t} = \theta(L)e_{t}, d\in (0,0.5), where e_{t} is a white noise, can be approximated well by an autoregressive (AR) model and establish the theoretical foundation of Haugh's (1976) statistics to test two ARFIMA processes being uncorrelated. The Haugh statistic is useful because it can avoid the issues of spurious regression induced by the long memory processes considered by Tsay and Chung (2000). Using AIC or Mallow's C_{p} criterion as a guide, we demonstrate through Monte Carlo studies that a lower order AR(k) model is sufficient to prewhitten an ARFIMA process and the Haugh test statistics after AR pre-whitening perform very well in finite sample. We illustrate the use of our methodology by investigating the independence between the volatility of two daily nominal dollar exchange rates-Euro and Japanese Yen. We find that there exists "strongly simultaneous correlation " between the volatilities of Euro and Yen within 30 days.; The second paper extends the analysis of Lewis and Reinsel (1985) to the r-dimensional I(d) process y_{t}, where d>0, i.e., we consider the problems of the linear prediction of y_{t+1} based on y_{t},y_{t-1},\dots, using a VAR model of order k fitted to a realization of T observations y_{1},y_{2},\dots,y_{T}. Assuming that k grows with T at a suitable rate, along with other regularity conditions imposed on y_{t}, the consistency of the multivariate least squares (LS) coefficient estimator and that of the residual covariance matrix estimator \widehat \Sigma_{k} are derived, and the one-step ahead prediction error based on the VAR(k) model is shown to converge in probability to its population counterpart.; Furthermore, a Monte Carlo experiment is carried out to assess the effect of estimating autoregressive parameters on the mean square prediction error. The results reveal that the average observed squared prediction errors from using the VAR(k) model are very close to the finite sample approximation formula \Sigma_{k}(h) derived by Lewis and Reinsel (1985) for the weakly dependent processes. |
| Keyword | long memory; approximation |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m1566 |
| Contributing entity | University of Southern California |
| Rights | Wang, Shin-Huei |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-Wang-2172 |
| Archival file | uscthesesreloadpub_Volume32/etd-Wang-2172.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | APPROXIMATING STATIONARY LONG MEMORY PROCESSES BY AN AR MODEL WITH APPLICATION TO FOREIGN EXCHANGE RATE by Shin-Huei Wang A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful¯llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2008 Copyright 2008 Shin-Huei Wang |
