Trend assessment in a long memory dependence model using the discrete wavelet transform

Craigmile, P.F., Guttorp, P. and Percival, D.B. (2004) Trend assessment in a long memory dependence model using the discrete wavelet transform. Environmetrics, 15(4), pp. 313-335. (doi:10.1002/env.642)

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Abstract

In this article we consider trend to be smooth deterministic changes over long scales, and tackle the problem of trend estimation in the presence of long memory errors (slowly decaying autocorrelations). Using the fractionally differenced (FD) process as a motivating example of such a long memory process, we demonstrate how the discrete wavelet transform (DWT) is a natural choice at extracting a polynomial trend from such an error process. We investigate the statistical properties of the trend estimate obtained from the DWT, and provide pointwise and simultaneous confidence intervals for the estimate. Based on evaluating the power in the trend estimate relative to the estimated errors, we provide a test of nonzero trend. We finish by applying the methods to a climatological example.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Craigmile, Dr Peter
Authors: Craigmile, P.F., Guttorp, P., and Percival, D.B.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Environmetrics
ISSN:1180-4009
ISSN (Online):1099-095X
Published Online:19 May 2004

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