Block Bootstrap Calibration with Application to the Fire Weather Index

Abstract

This article presents an analysis of Ontario Fire Weather Index (FWI) data^†

The data used is ©1963–2004, Queen’s Printer for Ontario, Canada, and was referenced under agreement with the Ontario Ministry of Natural Resources.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lssp.

using the block bootstrap for time series. Confidence intervals for parameters such as the first lag autocorrelation can have low coverage relative to the nominal level. Therefore, adjustments to the confidence intervals are necessary in order to achieve reasonable accuracy. We introduce a confidence interval calibration method in which the length of the confidence interval is adjusted according to an amount determined from a double bootstrap. We compare this method with the α-level adjustment method, and we find that the length-adjustment method is superior under scenarios similar to that of the FWI data: coverage proportions are slightly higher for the length-adjustment approach, and confidence interval widths are markedly smaller. Applying the length-adjustment method to the Ontario FWI data gives different results than would be obtained without adjustment.

Keywords:

• Autocorrelation
• Block bootstrap
• Calibration
• Double bootstrap
• Forest fire
• FWI
• Length adjustment
• Level adjustment
• Time series

Mathematics Subject Classification:

• Primary 62F40
• 62P12

Notes

The data used is ©1963–2004, Queen’s Printer for Ontario, Canada, and was referenced under agreement with the Ontario Ministry of Natural Resources.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lssp.