Abstract
The emergence of the power pool as a popular
institution for trading of power in different countries
has led to increased interest in the prediction of
power demand and price. We investigate whether the time
series of power-pool demand and price can be modelled
as the output of a low-dimensional chaotic dynamical
system by using delay embedding and estimation of the
embedding dimension, attractor-dimension or
correlation-dimension calculation, Lyapunov-spectrum
and Lyapunov-dimension calculation, stationarity and
nonlinearity tests, as well as prediction analysis.
Different dimension estimates are consistent and show
close similarity, thus increasing the credibility of
the fractal-dimension estimates. The Lyapunov spectrum
consistently shows one positive Lyapunov exponent and
one zero exponent with the rest being negative,
pointing to the existence of chaos. The authors then
propose a least squares genetic programming (LS-GP) to
reconstruct the nonlinear dynamics from the power-pool
time series. Compared to some standard predictors
including the radial basis function (RBF) neural
network and the local state-space predictor, the
proposed method does not only achieve good prediction
of the power-pool time series but also accurately
predicts the peaks in the power price and demand based
on the data sets used in the present study.
- (rbf)
- algorithms,
- analysis,
- and
- approximations,
- attractor-dimension,
- basis
- calculation,
- chaos,
- chaotic
- correlation-dimension
- delay
- demand
- demand,
- dimension,
- dynamical
- dynamics,
- embedding
- embedding,
- estimates,
- estimation,
- exponents,
- fractal
- fractal-dimension
- fractals,
- function
- genetic
- gp,
- least
- local
- low-dimensional
- lyapunov
- lyapunov-dimension
- lyapunov-spectrum,
- markets,
- methods,
- model
- net
- network,
- neural
- nonlinear
- nonlinearity
- power
- power-pool
- prediction
- prediction,
- predictor,
- price
- price,
- programming,
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