Simple Methods and Procedures Used in Forecasting
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1 Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria Jadamus-Hacura
2 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!
3 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
4 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
5 The data that has been analyzed in the Project are : - number of born Baby s in Germany - analyzed period starts from 1990 to the Data was taken from the Website of the German Census Office
6 Linear Trend Analysis Linear Trend y = t R 2 = 0, empircal data Linear (empircal data)
7 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 )
8 SUMMARY OUTPUT Regression Statistics Multiple R 0, R Square 0, Adjusted R Square 0, Standard Error 24085,46 V= 3,16% Observations 18 ANOVA df SS MS F Significance F Regression , ,50673E-08 Residual ,1 Total Coefficients Standard Error t Stat P-value Lower 95% Intercept , , , ,35626E ,6012 t , , , ,50673E ,9295
9 Linear Trend Analysis Linear trend equation: ) Y = , ,27* t Y ) - 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 on average in each year.
10 Measures of fit -The Coefficient of Determination R2 -Standard Error of Estimate Su - Coefficient of random variation V
11 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.
12 Standard Error of Estimate S u = 24085,46 It is the standard deviation around the trend line of the predicted values of Y.
13 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.
14 Predicted Value We estimate the value of born baby s in the year 2008 by extrapolation trend function for t = 19 : ) Y = , , 27*19 = ,34 The real number of born baby s in Germany in the year 2008 is The ex post error of estimation is equal to : ,34 = 11439,7 This error is less than estimated from the regression model. ( S u = 24085,5 )
15 Exponential Smoothing 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.
16 Brown's Linear (double) Exponential Smoothing forecast actual smoothed data
17 Brown's quadratic (triple) smoothing model data forecasts
18 Holt's method double exponential smoothing forecast actual smoothed data
19 Nonlinear smoothing model forecast actual smoothed data
20 Summary of Results MAE Forecasted value for 2008 ex post error absolute value of ex post error 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
21 Summary of Results ( graphically ) forecasted value real value Brown's Linear (double) Exponential Smoothing Brown's quadratic (ie, triple) smoothing model Holt's method double exponential smoothing Nonlinear smoothing model
22 General Comparison (graphically) Forecasted value for 2008 real value MAE absolute value of ex post error Brown's Linear (double) Exponential Smoothing Brown's quadratic (ie, triple) smoothing model Holt's method double exponential smoothing Nonlinear smoothing model Trend model Brown's Linear (double) Exponential Smoothing Brown's quadratic (ie, triple) smoothing model Holt's method double exponential smoothing Nonlinear smoothing model Trend model
23 THANK YOU FOR LISTENING
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