Simple Methods and

Procedures Used in

Forecasting

The project prepared by : Sven GingelmaierMichael Richter

Under direction of the Maria Jadamus-Hacura

Prediction of future events and conditions are called forecasts, and the act of making such

prediction is called forecasting.(WordNet Dictionary )

What Is Forecasting?

Sales will be $200 million!

Forecasting Methods Used in the Project :

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, denoted by { Yt : t ∈ N} , is a sequence of observations on particular variables.

Decomposition of time series data (classical decomposition):

TrendSeasonal TrendCyclical MovementsIrregular Components

Time Series AnalysisTime Series Analysis

The data that has been analyzed in theProject are :- number of born Baby´s in Germany - analyzed period starts from 1990 to2007

- the Data was taken from the Website of the German Census Office

Linear Trend Analysis

Linear Trend

y = -10405t + 860988R2 = 0,8497

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empircal data Linear (empircal data)

Linear Trend Analysis

We applied Ordinary Least SquaresMethod ( OLS ) to estimate coefficientsand the measures of fit of the linear trend model .We utilized Excel regression option forcalculation . ( Tools / Data Analysis / Regression )

Multiple R 0,9217700R Square 0,8496599Adjusted R Square 0,8402637Standard Error 24085,46 V= 3,16%Observations 18

ANOVAdf SS MS F Significance F

Regression 1 52456625447 52456625447 90,42538644 5,50673 E-08Residual 16 9281751953 580109497,1Total 17 61738377400

Coefficients Standard Error t Stat P-value Lower 95%Intercept 860988,4379 11844,32006 72,69209493 1,35626E-21 835879,6012t -10405,26832 1094,228689 -9,509226385 5,50673E-08 -12724,9295

SUMMARY OUTPUT

Regression Statistics

Linear Trend Analysis

860988,43 10405,27*Y t= −)

Linear trend equation:

Interpretation of slope coefficient :

Here b1 = 10405,27 tells us that the averagevalue of born baby´sdecreases by 10405 on average in each year .

Y)

- Estimated or predicted value of born baby´s

Measures of fit

-The Coefficient of Determination R2

-Standard Error of Estimate Su

- Coefficient of random variation V

Coefficient of

Determination, R2

The coefficient of determination is the portion of the total variation in the dependent variable that is explained by variation in the independent variableIn our example R2 =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

Su = 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 year2008 by extrapolation trend function for t = 19 :

860988,43 10405,27*19 663288,34Y = − =)

The real number of born baby´s in Germany in the year 2008 is674728 .

Theex post error of estimation is equal to :

674728 – 663288,34 = 11439,7

This error is less than estimated from the regression model .

( Su = 24085,5 )

Exponential Smoothing Exponential Smoothing Exponential Smoothing Exponential Smoothing

MethodsMethodsMethodsMethods

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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actual smoothed data

forecast

Brown's quadratic

(triple) smoothing model

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data forecasts

Holt's method double

exponential smoothing

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Nonlinear smoothing

model

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actual smoothed data

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Summary of Results

674728Real value of born baby´s in the

year 2008

3199-319967792716726Nonlinear smoothing

model

2337233767239117831Holt's method double exponential

smoothing

24271-2427169899929244Brown's quadratic ( triple) smoothing

model

1861-186167658919932Brown's Linear (double) Exponential

Smoothing

absolute value ofex post

errorex post

error

Forecasted valuefor

2008MAE

Summary of Results

( graphically )

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Brown's Linear(double) Exponential

Smoothing

Brown's quadratic(ie, triple) smoothing

model

Holt's method double exponential

smoothing

Nonlinear smoothingmodel

forecasted value

real value

General Comparison

(graphically)

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Brown's Linear(double)

ExponentialSmoothing

Brown'squadratic (ie,

triple) smoothingmodel

Holt's method double

exponentialsmoothing

Nonlinearsmoothing model

Trend model

Forecasted value for 2008

real value

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Brown'sLinear

(double)ExponentialSmoothing

Brown'squadratic (ie,

triple)smoothing

model

Holt's method double

exponentialsmoothing

Nonlinearsmoothing

model

Trend model

MAE

absolute value of ex posterror

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