Doctoral Dissertations

Keywords and Phrases

Prediction intervals


"The theory and methodology of obtaining bootstrap prediction intervals for univariate time series using the forward representation of the series is extended to vector autoregressive (VAR) models. Kim has shown that simultaneous prediction intervals based on the Bonferroni method and the backward representation of the time series achieve coverage close to nominal when the parameter estimates are corrected for small sample bias. To utilize his method, it is necessary to assume that the innovations are normally distributed to maintain independence of the innovations associated with the backward representation of the time series. This assumption is not necessary if the forward representation is used. Bootstrap prediction intervals based on the forward representation of the time series, are less restrictive and thus can also be adapted for time series that do not have a backward representation.

The asymptotic validity of the proposed bootstrap method is established and small sample properties are studied using Monte Carlo simulation. The simulation study also looks at a number of VAR models including stationary, unit root and near unit root processes. In these models, coverage close to nominal level is reached if the parameter estimates are corrected for small sample bias. In addition to the normal distribution, three non-normal distributions for the innovations are considered, namely the chi-squared, exponential and t distributions. Simulations where prediction intervals are obtained after conducting an order selection of a VAR(2) time series is also studied"--Abstract, page iii.


Samaranayake, V. A.

Committee Member(s)

Gadbury, Gary L.
Drain, David
Grow, David E.
Bryant, Richard Ralph


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics


University of Missouri--Rolla

Publication Date

Summer 2005


x, 170 pages

Note about bibliography

Includes bibliographical references (pages 168-169).


© 2005 Florian Sebastian Rueck, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

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

Thesis Number

T 8822

Print OCLC #


Included in

Mathematics Commons