Time Series Forecasting: A Multivariate Stochastic Approach

This note deals with a multivariate stochastic approach to forecast the behaviour of a cyclic time series. Particular attention is devoted to the problem of the prediction of time behaviour of sunspot numbers for the current 23th cycle. The idea is to consider the previous known n cycles as n particular realizations of a given stochastic process. The aim is to predict the future behaviour of the current n+1th realization given a portion of the curve and the structure of the previous n realizations. The model derived is based on the cross-correlations between the current n+1th realization and the previous n ones and the solution of the related least squares problem. As example we applied the method to smoothed monthly sunspots numbers from SIDC archives, in order to predict the behaviour of the current 23th solar cycle.