Seasonal Forecasting
The demand curve in a time-series analysis for any product, assuming
that it is not stable, is related to some opening level, a growing or declining
trend, season factors, cyclical factors, and irregularities. In the simplest
of models, let us first assume that the demand curve for our product changes
linearly with time, and let us define xt
as the actual demand for a period t (for n actual historical
observations, such that t = 1, 2, 3,… , n), a as the level,
b as the trend, and et as irregularities. Then,We shall use a least squares criterion in order to estimate values, denoted by , , and for the parameters of xt, a, and b. The model is now,
The least-squares criterion involves the selection of such denotations to minimize the sum of the squares of the n differences between xt and . In other words,
Via calculus and without proof, we shall state that
and
(under construction)