Spectral properties of temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.

Joint dynamic probabilistic constraints with projected linear decision rules

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (in nite dimensional) problem and approximating problems working with projections from di erent subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.