Multivariate Seasonal Time Series Forecast with Application to Adaptive Control

Abstract

A general multivariate model for seasonal riverflow is proposed. The formulation relates discharge at a particular station to current discharge at other stations as well as previous discharges at any station. Additionally, the formulation allows for moving average terms and accounts for seasonality in the mean and variance. An identification strategy is suggested and two general parameter estimation algorithms are discussed. A technique to obtain multi-lead forecasts from an identified model and the use of these to obtain approximate conditional Markovian transition matrices is given. The identification, estimation and validation of univariate and multivariate models is demonstrated using historical monthly discharges of the Nile basin. A new adaptive reservoir control algorithm which uses the approximate conditional Markovian transition matrices is also derived. It uses a dynamic programming formulation of the value iteration type with previous inflow and present storage as states. The number of stages over which the algorithm must be solved at each decision, and thus the computational burden, is dramatically reduced by using a tabulated boundary value function derived from the stationary control problem. The control algorithm is not evaluated in this work.