Bayesian prediction for stochastic processes
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Date
2016
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Abstract
In many fields of statistical analysis, one is not only interested in estimation
of model parameters, but in a prediction for future observations. For stochastic
processes, on the one hand, one can be interested in the prediction for the further
development of the current, i.e. observed, series. On the other hand, prediction
for a new series can be of interest. This work presents two Bayesian prediction
procedures based on the transition density of the Euler approximation, that include
estimation uncertainty as well as the model variance. In a first algorithm,
the pointwise predictive distribution is calculated, in a second, trajectories will
be drawn. Both methods will be compared and analyzed with respect to their
advantages and drawbacks and set in contrast to two commonly used prediction
approaches.
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Keywords
stochastic differential equation, predictive distribution, (jump) diffusion