ISE-410 Midterm Notes
Chapter 4: Forecasting
Causal Factor
: something that influences the data in a known way and can be helpful in
forecasting.
Processes
:
•
Constant Process
: plotted data is roughly level with some small variations.
o
Should have some reason to assume a process is constant
o
If the variance changes over time, the assumption of a constant process isn’t valid
•
Trend Process
: a process with a growth stage (sales increase) and/or a decline or phase-
out stage (sales are decreasing).
o
Assuming a constant process in either case can be disastrous
o
Can be linear or nonlinear
•
Seasonal Process
: a process where the pattern seems to repeat
o
Weather is often an underlying cause
o
Seasonal and cyclical are the same thing
•
There will always be some part that is unexplainable
Models
:
•
Generally have the form: d
t
= f(x
t-k
) + ε
t
o
d
t
= dependent variable
o
x
t
=
independent variable (causal factor)
o
ε
t
= noise component at time t
•
Constant: d
t
= a + ε
t
o
a = constant portion
o
Constant processes should have a constant mean
o
Estimates of future demand should be independent of how far in the future we
look
•
Linear trend: d
t
= a + bt + ε
t
o
b = trend
•
Seasonal: d
t
= ac
t
+ ε
t
o
c
t
= seasonal factor
Simple Linear Regression
: d
t
= a + bh
t
+ ε
t
t = 1, 2,…, n
•
a = intercept of the straight line relating d
t
and h
t
•
b = slope of the line
•
n = total number of months of data available
•
â = estimate of a
o
value of the dependent variable when the independent variable is zero
not necessarily a meaningful number
o
if zero is not a possible value of the independent variable, â may still be positive
in this case, â calibrates the other values
•
bhat = estimate of b (can be positive or negative)

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positive: dependent variable increases as the independent variable increases
(positive correlation)
o
magnitude should reflect the amount of change in the dependent variable for a
unit change in the independent variable
•
Coefficient of Determination
: r
2
(p. 106 in the text)
o
Coefficient of determination of .85 is considered quite good
•
Regression models are very useful for forecasting when there is a strong relationship and
a time lag between the dependent variable and the independent variable(s)
o
If they occur in the same time period, we can’t forecast future values of the
dependent variable unless we use a forecast of the independent variable
This introduces error in the forecast of the dependent variable
•
Extrapolating regression results can be dangerous
o
Statistically, only values in the range of the data used to fit the equation should be
used to forecast
•
If causal relationships do not exist, regression is NOT the best forecasting method
o
Be careful; often the cause and effect relationship isn’t clear
Trend Series Methods
: time-ordered list of historical data
•
Favored for short-term forecasting
•
History is a reasonable predictor of the future
•
Includes constant, trend, or seasonal models

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