Nonlinear Time Series Modelling: Order
Identification and Wavelet Filtering
by Alwell J. Oyet
.
Abstract:
In this paper we discuss an approach for modelling nonlinear
time series data based on wavelet smoothing.
The technique involves decomposing the series into two components - a
deterministic component which when extracted by wavelet filtering
leaves a random component which can be easily modelled
using well known linear time series modelling techniques or by a
simple diagonal pure bilinear
model discussed in this paper. The two components are then combined to
describe the series. We also discuss how patterns present in the third order
cumulants of the diagonal pure bilinear time series model can be used to
identify the order of the model. Simulated data and real time series
examples are used to illustrate the techniques.
Key Words:
Bilinear time series; Daubechies wavelet; Difference equation;
Order identification; Standardized cumulant trace; Wavelet filtering
Author:
Alwell J. Oyet,
aoyet@math.mun.ca
Editor:
Abdulnasser J. Hatemi
,
abdulnasser.hatemi-j@ihh.hj.se
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