Abstract:

Given m time series regression models, linear or not, with additive noise components, it is shown how to estimate the predictive probability distribution of all the time series conditional on the observed and covariate data at the time of prediction. This is done by a certain synergy argument, assuming that the distributions of the residual components associated with the regression models are tilted versions of a reference distribution. Point predictors are obtained from the predictive distribution as a byproduct. Applications to US mortality rates prediction and to value at risk (VaR) estimation will be discussed. A connection with harmonic analysis will be pointed to.