2.2 Statistical model

Exponential Smoothing

Among the forecast equations for all time series-based estimates, the exponential smoothing (a popular scheme to produce smoothed time series) is a relatively simple prototype model for forecasting, analysis and re-analysis of environmental variables  (Box, 1991;  \citealp{m2008}). This technique uses historical time series data under the assumption that the future will like resemble the past, in an attempt to identify specific patterns in the data and then project and extrapolate those patterns into the future (without using the model to identify the causes of patterns). Compared to other techniques (e.g. moving averages), which equally weight past observations, exponential smoothing apportions exponentially decreasing weights as observations get older. This means that recent observations are given relatively more weight in forecasting than older observations. To compute predictions based on the observed time series of PDSI data, we make use of our knowledge concerning the period of the system under investigation (e.g. \citealp*{Wichard2005}). The following periodic simple exponential smoothing \cite{Taylor2003} was selected as reference model for time-pattern propagation into the future: