Doctoral Dissertations

Keywords and Phrases

Autoregressive Integrated Moving Average (ARIMA); Fractional Auto-Regressive Integrated Moving Average (FARIMA)

Abstract

"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for such processes are established, and the finite sample properties are examined by employing Monte Carlo simulations. The Monte Carlo simulation study shows that the proposed method works well for both ARIMA and FARIMA processes. Following the existing sieve bootstrap frame-work for testing unit roots for nonseasonal processes, we propose new bootstrap-based unit root tests for seasonal time series. In this procedure, the bootstrap distributions of the well known Dickey-Hasza-Fuller (DHF) seasonal test statistics are obtained and utilized to determine the critical points for the test. The asymptotic properties of the proposed method are established and a Monte Carlo simulation study is employed to demonstrate that the proposed unit root tests yield higher powers compared to the DHF test. Also, a sieve bootstrap method is implemented to obtaining prediction intervals for time series with seasonal unit roots. The asymptotic properties of the proposed prediction intervals are established and a Monte Carlo simulation study is carried out to examine the finite sample validity. Finally, we derive expressions for the asymptotic distributions of the Dickey-Fuller (DHF) type test statistics, under weakly dependent errors and show that they can be expressed as functional of the standard Brownian motions. Currently, the asymptotic results are available only for non-seasonal time series"--Abstract, page v.

Advisor(s)

Samaranayake, V. A.

Committee Member(s)

Adekpedjou, Akim
Gelles, Gregory M.
Paige, Robert
Wen, Xuerong

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics and Statistics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2012

Journal article titles appearing in thesis/dissertation

  • Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes
  • Obtaining prediction intervals for FARIMA processes using sieve bootstrap
  • Prediction intervals for ARIMA processes: a sieve bootstrap approach
  • Asymptotic distributions of the Dickey-Hasza-Fuller seasonal unit root tests under weakly dependent errors
  • Sieve bootstrap for seasonal time series: unit root tests and prediction intervals

Pagination

xii, 141 pages

Note about bibliography

Includes bibliographical references.

Rights

© 2012 Maduka Nilanga Rupasinghe, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Bootstrap (Statistics)Prediction (Logic)Time-series analysis

Thesis Number

T 10035

Print OCLC #

815768135

Electronic OCLC #

808468425

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