Transcript CHAPTER 4 SIMPLE SMOOTHING METHODS

Forecasting Formulas Symbols
n
Total number of periods, or number
of data points.
A
Actual demand for the period (Y).
F
Forecast demand for the period (Y).
Y
Dependent variable, or actual demand
(Y = Actual, Y = Forecast).
e
Error.
T
Trend factor.
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C
Cyclical factor.
S
Seasonal factor.
Y
Forecast dependent variable.
a
Y intercept.
b
Slope of the line.

Alpha. The desired response rate,
or smoothing constant.
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(P)
Probability.
P
Mean proportion of a large
sample.

Sigma standard deviation of
the population.
x
Independent variable.
y
Dependent variable data point.
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t
Mean of the error for a time interval.
t
Error for a single time period.
Z
Value from normal distribution (i.e.
number of standard deviation
from the expected distribution).
S
Standard deviation of the errors.
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R2
Coefficient of determination (The
percentage of exploised, eliminated
and removed variances).
Z
MAD
Mean absolute deviation.
I
Index.

mu  population mead.
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
Sx =  (X -X)2/(n-1)
Sample standard deviation of X.

x =  (X - )2 /N
Population standard deviation of X.

Syx =  (Yt -Yt)2/(n-r)
Standard deviation of estimate  standard
deviation of forecast errors. (n = number of
observations, r = smoothing) or regression (2)
(a & b) indicators).
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Syx = S
Standard deviation of estimate
 standard deviation of the
Errors.
t = At - Ft
Forecast error for period t =
actual demand for period t
less the (should be ~ ND
(0,low) forecast demand for
period t.
Ft = Ft-1 +  (At-1 – Ft-1)
The exponentially
smoothed forecast
for period t = the exponentially smoothed
forecast for the prior period + the smoothing
constant times (the actual for the prior period
less the forecast for the prior period).
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Yt = a + bt
Forecast: Simple Linear
Trend.
Yt = a + bt + ct2
Forecast: Quadratic
Trend.
Yt = T CI SI I
Decomposition model:
Forecast value = Trend
times cyclical indicators times seasonal
indicator times irregular indicator.
Yt = T SI
Simple Decomposition model:
Forecast value = Trend times
seasonal indicator.
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2 x+y = 2 x + 2 y
Standard deviation squared for x + y =
the standard deviation of x + the standard
deviation of y.
 x+y =  x +  y
 et - 0
TS = 
MAD
Population mean for
x + y = the mean of
x + the mean of y.
Tracking signal = the total
of errors/MAD.
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t - 0
Z = 
S
Z – value for
errors = the mean of the
errors for a time interval
over the standard deviation
of the errors.
 APE
MAPE = 
n
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MAD = 0.8Se
Mean absolute deviation
= 0.8 times the standard
deviation of the forecast
errors.
S = MAD (1.25)
Standard deviation of
the forecast errors =
mean absolute deviation
times 1.25.
t = 0  Z S
Confidence interval for
errors = times standard
deviation of the forecast
errors.
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APE=
A - F
|
 A 
Absolute value of actual less forecast divided
by actual.
Syx 2
R2 = 1 - 
sy 2
The coefficient of se2
determination = 1 - 
sy 2
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sy2-s2
R2 = 
sy2
The coefficient of
determination.
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