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# Prediction of a nonlinear time series with feedforward neural networks - PowerPoint PPT Presentation

Prediction of a nonlinear time series with feedforward neural networks. Mats Nikus Process Control Laboratory. The time series. A closer look. Another look. Studying the time series. Some features seem to reapeat themselves over and over, but not totally ”deterministically”

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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

### Studying the time series

• Some features seem to reapeat themselves over and over, but not totally ”deterministically”

• Lets study the autocovariance function

### Studying the time series

• 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

### The phase plots tell

• 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.

### The neural network

^

y(k+1)

Lets try with 3 hidden nodes

2 for the ”parabola”

and one for the ”rest”

y(k) y(k-1)

### A more difficult case

• 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.

### Use a Kalman-filter to update the weights

• We can improve the predictions by using a Kalman-filter

• Assume that the process we want to predict is described by

### Kalman-filter

• Use the following recursive equations

Ck is fairly simple to

calculate for a sigmoidal

network

### Henon series

• The timeseries is actually described by