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The paper presents the fundamental theory
of neural networks, and treats the neural network's properties as a
non-linear estimator, especially with respect to financial time-series data.
In specific the CAPM-model with time-varying covariances
is used.
The financial time-series are represented by three
ARMA-processes, plus one univariate and two multivariate GARCH-in-mean specified CAPM-models.
It is found, that the neural network is a consistent
estimator, and that the performance in homoscedastic
models is quite good. In models with heteroscedasticity
and low signal/noise relation the performance is not very good. Even
against a grossly misspecified univariate
estimation of a multivariate GARCH-in-mean CAPM-model, the performance of the
neural network is worse than that of the misspecified
model's.
A number of possible CAPM-consistent corrections for heteroscedasticity are proposed,
that may improve the efficiency of the neural network as an estimator.
The applicability of the neural network as a non-linear
estimator is absolutely not to be rejected based on the results found in this
paper.
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