Prediction of a nonlinear time series with feedforward neural networks

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Prediction of a nonlinear time series with feedforward neural networks

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Prediction of a nonlinear time series with feedforward neural networks

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Prediction of a nonlinear time series with feedforward neural networks

Mats Nikus

Process Control Laboratory

- Some features seem to reapeat themselves over and over, but not totally ”deterministically”
- Lets study the autocovariance function

- The autocovariance function tells the same: There are certainly some dynamics in the data
- Lets now make a phaseplot of the data
- In a phaseplot the signal is plotted against itself with some lag
- With one lag we get

- Use two lagged values
- The first lagged value describes a parabola
- Lets make a neural network for prediction of the timeseries based on the findings.

^

y(k+1)

Lets try with 3 hidden nodes

2 for the ”parabola”

and one for the ”rest”

y(k) y(k-1)

- If the time series is time variant (i.e. the dynamic behaviour changes over time) and the measurement data is noisy, the prediction task becomes more challenging.

- We can improve the predictions by using a Kalman-filter
- Assume that the process we want to predict is described by

- Use the following recursive equations

The gradient needed in

Ck is fairly simple to

calculate for a sigmoidal

network

- The timeseries is actually described by