7. UNIVARIATE MODEL FORECASTING › 7.4 Analytic Technique Tutorial › 7.4.1 Linear, Quadratic, and Cubic Models

7.4.1 Linear, Quadratic, and Cubic Models

Univariate Model Forecasting allows you to evaluate models
that involve linear, quadratic, and cubic functions of time.
The characteristics of these models are as follows:

o  A linear model proposes that the data element can be
   modeled based on the interval number (that is, time
   period).  Linear models are considered to be the most
   reliable for the short series of historical observations
   that you normally encounter.  The general form of a linear
   model is shown in the following equation:

      y = m * x + b                              (Eqn 7)

   where y is the data element, x is the interval number,
   m is the coefficient of x (that is, the slope), and b
   is the intercept.

o  A quadratic model proposes that the data element can be
   modeled based on the interval number squared.  The general
   form of the quadratic model is shown in the following
   equation.

                 2
      y = m1 * x  + m2 * x + b                    (Eqn 8)

   where y is the data element, x is the interval number, m1
   and m2 are the coefficients of the interval numbers, and b
   is the intercept.

o  A cubic model proposes that the data element can be
   modeled based on the interval number cubed.  The general
   form of the cubic model is shown in the following
   equation.

                 3         2
      y = m1 * x  + m2 * x  + m3 * x + b          (Eqn 9)

   where y is the data element, x is the interval number, m1,
   m2, and m3 are the coefficients of the interval numbers,
   and b is the intercept.

You should avoid higher order models (that is, quadratic and
cubic) for historical data series that include less than 30
historical observations because these models are often
unreliable when they are based on a small number of
observations.  With shorter series, these models have a
propensity to select coefficients for their equations that
almost ideally represent the historical data points but
rapidly diverge beyond the range of the historical
observations.