Time series forecasting means the prediction of future values based upon a collection of present and past values. Accurate forecasting is of importance in many fields, as for instance for government activities, in the industry, which deal with predictions of future revenues, costs, demands, a.o. [123].
A time-series X(t) is defined as a series of values
where t is a discrete time variable.
Prediction for a time series can be defined as follows:
Given a time series X(t) and a moment in time t, there is to be determined the value of the series at the point t+1, as a function of some of the previous values:
where
