Department of Adaptive Systems

In an AR(p) model of data evolution in a discrete time with a Gaussian noise uncorrelated between the data channels, we are trying to predict the distribution of data up to the horizon t + h, knowing the data at time t. Because of the use of Bayesian paradigm, there is a parameter uncertainty present in the model specified by a known prior distribution.
Since the analytical solution of such a prediction is not tractable due to the high dimensionality of the problem (in this case the dimension is in nine), we are forced to search for approximative solutions. We propose one such solution using Monte Carlo sampling from the prior distribution and later reconstruction of the final distribution.