By Topic

Wavelet-based parameter estimation for polynomial contaminated fractionally differenced processes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Craigmile, P.F. ; Dept. of Stat., Ohio State Univ., Columbus, OH, USA ; Guttorp, P. ; Percival, D.B.

We consider the problem of estimating the parameters for a stochastic process using a time series containing a trend component. Trend, i.e., large scale variations in the series that are best modeled outside of a stochastic framework, is often confounded with low-frequency stochastic fluctuations. This problem is particularly evident in models such as fractionally differenced (FD) processes, which exhibit slowly decaying autocorrelations and can be extended to encompass nonstationary processes with substantial low frequency components. We use the discrete wavelet transform (DWT) to estimate parameters for stationary and nonstationary FD processes in a model of polynomial trend plus FD noise. Using Daubechies wavelet filters allows for automatic elimination of polynomial trends due to embedded differencing operations. Parameter estimation is based on an approximate maximum likelihood approach made possible by the fact that the DWT decorrelates FD processes approximately. We consider this decorrelation in detail, examining the between- and within-scale wavelet correlations separately. Better between-scale decorrelation can be achieved by increasing the length of the wavelet filter, whereas the within-scale correlations can be handled via explicit modeling by a low-order autoregressive process. We demonstrate our methodology by applying it to a popular climate dataset.

Published in:

Signal Processing, IEEE Transactions on  (Volume:53 ,  Issue: 8 )