Soner Bekleric Title of Thesis: Nonlinear Prediction via Volterra Ser

2.4. 1-D SYNTHETIC AND REAL DATA EXAMPLES 20
Walker equations and Burg’s method with parameter p = 4. Figures 2.3 (d) and 2.3
(e) portray predicted data using linear prediction theory (p = 4) and the associated
modeling error (which is equivalent to the difference between the original data and
the predicted data), respectively. It is clear that the three different prediction
algorithms provide similar results. I did not plot differences between original data
and these methods (Yule-Walker and Burg’s) because the results were quite similar
to those obtained in Figure 2.3 (e).
I also attempt to model data corresponding to the so called Arctic oscillation
(AO)-a time series from 1950 to 1999 of sea level pressures. These data are used to
characterize the long term variability of nonseasonal sea level oscillations (Thomson,
2004).
Figure 2.4 (a) shows nonlinear AO-a data for a period from 1950 to 1999. The
data consist of 104 samples (3 observations per year-January, February, March).
Figures 2.4 (b) and 2.4 (c) illustrate predicted AO values using Yule-Walker equa-
tions and Burg’s algorithm with linear terms (p = 14). Figures 2.4 (d) and 2.4 (e)
represent our attempt to model the data with a linear prediction filter (p = 14) and
the modeling error, respectively. Again, it is clear that the dynamics of the time
series cannot be captured by linear prediction methods.