**Authors:** Michail Zak

One of the fundamental objectives of mathematical modeling is to interpret past and present, and, based upon this interpretation, to predict future. The use at time t of available observations from a time series to forecast its value at some future time t+l can provide basis for 1) model reconstruction, 2) model verification, 3) anomaly detection, 4) data monitoring, 5) adjustment of the underlying physical process. Forecast is usually needed over a period known as the lead time that is problem specific. For instance, the lead time can be associated with the period during which training data are available. The accuracy of the forecast may be expressed by calculating probability limits on either side of each forecast. These limits may be calculated for any convenient set of probabilities, for example, 50% and 90%. They are such that the realized value of the time series, when it eventually occurs, will be included within these limits with the stated probability.

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[v1] 2014-06-16 18:39:38

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