Prediction of a nonlinear time series with feedforward neural networks

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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

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