Simple Methods and Procedures Used in Forecasting

Simple Methods and
Procedures Used in
Forecasting
The project prepared by : Sven Gingelmaier
Michael Richter
Under direction of the Maria Jadamus-Hacura

What Is Forecasting?
Prediction of future events and conditions are
called forecasts, and the act of making such
prediction is called forecasting.
(WordNet Dictionary )
Sales will be $200
million!

Forecasting Methods Used in
the Project :
Linear trend model
Exponential smoothing models :
- Brown´s linear exponential smoothing
- Browns quadratic smoothing model
- Holt´s method double exponential smoothing
- Nonlinear smoothing model

Time Series Analysis
Time series, denoted by { Y t : t ∈ N} , is a
sequence of observations on particular
variables.
Decomposition of time series data (classical
decomposition):
Trend
Seasonal Trend
Cyclical Movements
Irregular Components

The data that has been analyzed in the
Project are :
- number of born Baby´s in Germany
- analyzed period starts from 1990 to
2007
- the Data was taken from the Website
of the German Census Office

Linear Trend Analysis
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Linear Trend
y = -10405t + 860988
R 2 = 0,8497
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
empircal data Linear (empircal data)

Linear Trend Analysis
We applied Ordinary Least Squares
Method ( OLS ) to estimate coefficients
and the measures of fit of the linear
trend model .
We utilized Excel regression option for
calculation . ( Tools / Data Analysis /
Regression )

SUMMARY OUTPUT
Regression Statistics
Multiple R 0,9217700
R Square 0,8496599
Adjusted R Square 0,8402637
Standard Error 24085,46 V= 3,16%
Observations 18
ANOVA
df SS MS F Significance F
Regression 1 52456625447 52456625447 90,42538644 5,50673E-08
Residual 16 9281751953 580109497,1
Total 17 61738377400
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 860988,4379 11844,32006 72,69209493 1,35626E-21 835879,6012
t -10405,26832 1094,228689 -9,509226385 5,50673E-08 -12724,9295

Linear Trend Analysis
Linear trend equation:
Y )
)
Y = 860988,43 −10405,27*
t
- Estimated or predicted value of born baby´s
Interpretation of slope coefficient :
Here b 1 = 10405,27 tells us that the average
value of born baby´s decreases by 10405
on average in each year .

Measures of fit
-The Coefficient of Determination R2
-Standard Error of Estimate Su
- Coefficient of random variation V

Coefficient of
Determination, R 2
The coefficient of determination is the
portion of the total variation in the
dependent variable that is explained by
variation in the independent variable
In our example R 2 =0,8496.
It means that 84 % of the total variation of
the number of born baby´s is explained by
the trend model .

Standard Error of
Estimate
S u = 24085,46
It is the standard deviation around
the trend line of the predicted
values of Y.

Coefficient of random
variation
V = 3,16%
The value of standard error is around
3% of the mean of the number of born
baby´s .

Predicted Value
We estimate the value of born baby´s in the year
2008 by extrapolation trend function for t = 19 :
)
Y = 860988,43 − 10405, 27*19 = 663288,34
The real number of born baby´s in Germany in the year 2008 is
674728 .
The ex post error of estimation is equal to :
674728 – 663288,34 = 11439,7
This error is less than estimated from the regression model .
( S u = 24085,5 )

Exponential Exponential Exponential Smoothing
Smoothing
Methods
Methods
Exponential smoothing has become
very popular as a forecasting method
for a wide variety of time series data.
The predicted value in this method is a
weighted average of past observations .
Weights decay geometrically as we go
backwards in time .

Brown's Linear (double)
Exponential Smoothing
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
actual smoothed data
forecast

Brown's quadratic
(triple) smoothing model
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
data forecasts

Holt's method double
exponential smoothing
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forecast
1 3 5 7 9 11 13 15 17 19 21 23
actual smoothed data

Nonlinear smoothing
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model
1 3 5 7 9 11 13 15 17 19 21 23
actual smoothed data
forecast

Summary of Results
Brown's Linear (double) Exponential
Smoothing
Brown's quadratic ( triple) smoothing
model
Holt's method double exponential
smoothing
Nonlinear smoothing
model
Real value of born baby´s in the
year 2008
MAE
19932
29244
17831
16726
Forecasted
value
for
2008
676589
698999
672391
677927
674728
ex post
error
-1861
-24271
2337
-3199
absolute
value of
ex post
error
1861
24271
2337
3199

Summary of Results
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( graphically )
Brown's Linear
(double) Exponential
Smoothing
Brown's quadratic
(ie, triple) smoothing
model
Holt's method
double exponential
smoothing
forecasted value
real value
Nonlinear smoothing
model

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General Comparison
Brown's Linear
(double)
Exponential
Smoothing
Brown's
quadratic (ie,
triple) smoothing
model
(graphically)
Holt's method
double
exponential
smoothing
Forecasted value for 2008
real value
Nonlinear
smoothing model
Trend model
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10000
5000
0
Brown's
Linear
(double)
Exponential
Smoothing
Brown's
quadratic (ie,
triple)
smoothing
model
Holt's method
double
exponential
smoothing
MAE
absolute value of ex post
error
Nonlinear
smoothing
model
Trend model

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