Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 49

information can often be obtained from a visual examination of the plots, which
helps in selecting the most appropriate forecasting procedure. In addition to
calculating the best forecasts, it is also important to specify the accuracy with
which the forecasts are to be determined, so that the risk associated with decisions
based upon the forecasts may be calculated.

2.9.2 Forecasting Using Trend Analysis

For trend forecasting, linear or nonlinear regression is mostly used. This is based
on trend line fitting of time series data using a linear, quadratic, or exponential
function

x xb

p

2

x ax bx c

p

x exp[ ax b ]

p

2.9.3 Forecasting Using Regression Approaches

Regression analysis is a mathematical tool that supports the study of relationships
among the observed variables. Its main objective is to estimate and predict the
value of one variable by taking into account the values of the possibly related other
observed variables. Thus, before using the regression technique for prediction of a
specific variable, all variables related to this variable should be identified. For
prediction

x simple regression
x multiple regression
x nonlinear regression
can be used.
Forecasting using simple regression is based on the equation

YaaX H , where i = 1, 2, …, n ;

i 0 1 i i

where the mean value of the error H is supposed to be zero, and its variance is
one. The unknown values of parameters a 0 and a 1 should be estimated so that

n

2

¦ ( ya ax )

i 0 1 i

i 1

is minimized. This can be achieved in a straight-forward way by differentiating the
above sum with respect to the parameters a 0 and a 1 .
In the majority of practical cases, multiple regression is used as a mutual
relation