Chaotic system reconstruction from noisy time series measurements using improved least squares genetic programming

2003 ◽  
Author(s):  
V. Varadan ◽  
H. Leung
Keyword(s):  
Time Series ◽  
Genetic Programming ◽  
Least Squares ◽  
Chaotic System ◽  
Noisy Time Series ◽  
System Reconstruction

MEASURING THE PREDICTABILITY OF NOISY RECURRENT TIME SERIES

1993 ◽  
Vol 03 (03) ◽  
pp. 797-802
Author(s):  
R. WAYLAND ◽  
D. PICKETT ◽  
D. BROMLEY ◽  
A. PASSAMANTE
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Additive Noise ◽  
Nearest Neighbor ◽  
Least Squares Method ◽  
Total Least Squares ◽  
Short Time Series ◽  
Forecasting Method ◽  
Noisy Time Series ◽  
Short Time

The effect of the chosen forecasting method on the measured predictability of a noisy recurrent time series is investigated. Situations where the length of the time series is limited, and where the level of corrupting noise is significant are emphasized. Two simple prediction methods based on explicit nearest-neighbor averages are compared to a more complicated, and computationally expensive, local linearization technique based on the method of total least squares. The comparison is made first for noise-free, and then for noisy time series. It is shown that when working with short time series in high levels of additive noise, the simple prediction schemes perform just as well as the more sophisticated total least squares method.

scholarly journals Identification of an unstable ARMA equation

2001 ◽  
Vol 7 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Yulia R. Gel ◽  
Vladimir N. Fomin
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Infinite Order ◽  
Time Series Model ◽  
Identification Algorithm ◽  
Data Handling ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Strongly Consistent ◽  
Minimal Phase

Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.

Neural network forecasting of short, noisy time series

1992 ◽  
Vol 16 (4) ◽  
pp. 293-297 ◽  
Author(s):  
W.R. Foster ◽  
F. Collopy ◽  
L.H. Ungar
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Noisy Time Series

Filtering financial time series by least squares

2012 ◽  
Vol 4 (2) ◽  
pp. 149-154 ◽  
Author(s):  
Adrian Letchford ◽  
Junbin Gao ◽  
Lihong Zheng
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Financial Time Series ◽  
Financial Time
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