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Forecasting

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Published in: Geography
4,773 Views

Methods of Forecasting 

Sandeep K / Kolkata

3 years of teaching experience

Qualification: M.Tech. (Production Engineering)

Teaches: Chemistry, English, Hindi, Physics, Drawing, Mechanical

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  1. Forecasting ER. SANDEEP KUMAR
  2. Eight Steps to Forecasting • • • • • • • • Determine the use of the forecast What objective are we trying to obtain? Select the items or quantities that are to be forecasted. Determine the time horizon of the forecast. Short time horizon — 1 to 30 days Medium time horizon — 1 to 12 months Long time horizon — more than 1 year Select the forecasting model or models Gather the data to make the forecast. Validate the forecasting model Make the forecast Implement the results ER. SANDEEP KUMAR 2
  3. Forecasting Models Forecasting Techniques Qualitative Models Delphi Method Jury of Executive Opinion Sales Force Composite Consumer Market Survey Causal Methods Simple Regression Analysis Multiple Regression Analysis ER. SANDEEP KUMAR Time Series Methods Naive OVI Average Moving Average x on la Smoothing Trend Analysis easona y Analysis Multiplicative Decomposition 3
  4. Model Differences Qualitative — incorporates judgmental & subjective factors into forecast. Time-Series — attempts to predict the future by using historical data. Causal — incorporates factors that may influence the quantity being forecasted into the model ER. SANDEEP KUMAR
  5. Qualitative Forecasting Models • Delphi method o Iterative group process allows experts to make forecasts Participants: • decision makers: 5-10 experts who make the forecast • staff personnel: assist by preparing, distributing, collecting, and summarizing a series of questionnaires and survey results • respondents: group with valued judgments who provide input to decision makers ER. SANDEEP KUMAR 5
  6. Qualitative Forecasting Models (cont) Jury of executive opinion Opinions of a small group of high level managers, often in combination with statistical models. Result is a group estimate. • Sales force composite Each salesperson estimates sales in his region. Forecasts are reviewed to ensure realistic. Combined at higher levels to reach an overall forecast. Consumer market survey. Solicits input from customers and potential customers regarding future purchases. Used for forecasts and product design & planning ER. SANDEEP KUMAR 6
  7. Forecast Error • Bias - The arithmetic sum of the errors • Mean Square Error - Similar to simple sample variance • Variance - Sample variance (adjusted for degrees of freedom) • Standard Error - Standard deviation of the sampling distribution • MAD - Mean Absolute MAD = Deviation • MAPE - Mean Absolute Percentage Error Forecast Error = A -F MSE = forecast error 12 /T t=l t=l t=l t=l -Ft I/ At]/T t=l ER. SANDEEP KUMAR 7
  8. Quantitative Forecasting Models Time Series Method o Naive • Whatever happened recently will happen again this time (same time period) • The model is simple and flexible • Provides a baseline to measure other models • Attempts to capture seasonal factors at the expense of ignoring trend ER. SANDEEP KUMAR : Quarterly data : Monthly data 8
  9. Naive Forecast Wallace Garden Supply 4.0 9.0 4.0 4.0 9.0 4.0 4.0 Forecasting Period January February March April May June July August September October November December Storage Shed Sa les Actual Value 10 12 16 13 19 15 20 22 19 21 19 Naive Forecast N/A 10 12 16 13 19 15 20 22 19 21 E rror 2 4 -3 4 2 -4 5 2 -3 2 -2 0.818 BIAS Absolute E rror 2 4 3 4 2 4 5 2 3 2 2 3 MAD Error 16.67 / 25.00/ 23.08/ 23.53/ 10.53/0 26.67 / 25.00/ 9.09/0 15.79/ 9.52 / 10.53/0 17.76/ MAPE Squared E rror 16.0 16.0 16.0 25.0 10.091 MSE 3.176619 Standard Error (Square Root of MSE) = ER. SANDEEP KUMAR 9
  10. Naive Forecast Graph Wallace Garden - bhive Forecast 25 20 15 10 5 February March April June July Period August Septerrber October Novermber Decenter ER. SANDEEP KUMAR Actual Value Nave Forecast 10
  11. Quantitative Forecasting Models Time Series Method Moving Averages • Assumes item forecasted will stay steady over time. • Technique will smooth out short-term irregularities in the time series. k k - period rmving average = (Actual value in previous k periods) /k ER. SANDEEP KUMAR 11
  12. Moving Averages Wallace Garden Supply Forecasting Storage Shed Sales Period January February March April May June July August September October November December Actual Val I-le 10 12 16 13 19 15 20 22 19 21 19 Three-Month Moving Averages 20 22 21 3 3 3 3 3 3 3 3 3 ER. SANDEEP KUMAR 12.67 13.67 15.33 16.33 17.00 18.00 19.00 20.33 20.67 12
  13. Moving Averages Forecast Wallace Garden Supply Actual Value Forecasting In ut Data Period Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 Next period 3 period moving average Forecast Error Anal sis Actual Value - Forecast 10 12 16 13 19 15 20 22 19 21 19 19.667 Forecast 12.667 13.667 15.333 16.333 17.000 18.000 19.000 20.333 20.667 Average E rror 0.333 3.333 3.667 -1.333 3.000 4.000 0.000 0.667 -1.667 12.000 BIAS Absolute error 0.333 3.333 3.667 1.333 3.000 4.000 0.000 0.667 1.667 2.000 MAD Squared error 0.111 11.111 13.444 1.778 9.000 16.000 0.000 0.444 2.778 6.074 MSE ER. SANDEEP KUMAR Absolute % error 2.56% 19.61% 19.30% 8.89% 15.00% 18.18% 0.00% 3.170/0 8.77% 10.610/ MAPE 13
  14. Moving Averages Graph 25 20 15 10 Three Period Moving Average 10 Time ER. SANDEEP KUMAR 11 Actual Value Forecast 12
  15. Quantitative Forecasting Models Time Series Method Weighted Moving Averages • Assumes data from some periods are more important than data from other periods (e.g. earlier periods). • Use weights to place more emphasis on some periods and less on others. k - period weighted moving average k k (Weight for each period i)(Actual value in previous k periods) / E (weights) ER. SANDEEP KUMAR 15
  16. Weighted Moving Average Wallace Garden Supply Forecasting Storage Shed Sales Period January February March April May June July August September October November December Next period Actual Value Weights Three-Month Weighted Moving Averages 10 12 16 13 19 15 20 22 19 21 19 20.185 0.222 0.593 0.185 2. 2 3 2 3 4. 3 1 .ooo 2 2 7.1 3 4.1 1 1 1 1 1 1 1 1 1 Sum of weights = ER. SANDEEP KUMAR 12.298 14.556 14.407 1 6.484 17.814 16.815 19.262 21 .ooo 20.036 16
  17. Weighted Moving Average Wallace Garden Supply Forecasting Input Data Period Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 3 period weighted moving average Forecast Error Analysis Actual value 10 12 16 13 17 19 15 20 22 19 21 19 20.185 Weights 0.222 0.593 0.185 1 .ooo Forecast 12.298 14.556 14.407 16.484 17.814 16.815 19.262 21 .ooo 20.036 Average Error 0.702 2.444 4.593 —1 .484 2.186 5.185 -0.262 0.000 -1.036 1.988 BIAS Absolute error o. 702 2.444 4.593 1 .484 2.186 5.185 0.262 0.000 1.036 6.952 MAD Squared error 0.492 5.971 21.093 2.202 4.776 26.889 0.069 0.000 1.074 6.952 MSE Next period Sum of weights = ER. SANDEEP KUMAR Absolute % error 5.40% 24.17% 9.89% 10.93% 23.57% 1.380/0 0.00% 5.45% 10.57% MAPE 17
  18. Quantitative Forecasting Models Time Series Method Exponential Smoothing Moving average technique that requires little record keeping of past data. • Uses a smoothing constant a with a value between 0 and 1. (Usual range 0.1 to 0.3) Forecast for period t = forecast for period t - + a(actual value in period t -1 - forecast for period t - 1) ER. SANDEEP KUMAR 18
  19. Exponential Smoothing Data Wallace Garden Supply 14) = 15) = Forecasting period January February March May June July August September October November December Actual Value 10 12 16 13 19 15 20 22 19 21 19 Storage Shed Sales Exponential Smoothing a 10 10 12 16 13 19 15 20 22 19 21 ER. SANDEEP KUMAR 10 10 10 11 11 12 12 13 13 Ft+l 10.000 10.200 10.780 1 1 .002 1 1 .602 12.342 12.607 13.347 14.212 14.691 15.322 19
  20. Exponential Smoothing Wallace Garden Supply Forecasting Input Data Period Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Month 11 Month 12 Alpha Next period Exponential smoothing Forecast Error Analysis Actual value 10 12 16 13 19 15 20 22 19 21 19 0.419 19.573 Forecast 10.000 10.000 10.838 13.000 13.000 14.675 16.487 15.864 17.596 19.441 19.256 19.987 Average Error 2.000 5.162 0.000 4.000 4.325 -1.487 4.136 4.404 -0.441 1 .744 -0.987 Absolute error 2.000 5.162 0.000 4.000 4.325 1.487 4.136 4.404 0.441 1 .744 0.987 2.608 MAD Squared error 4.000 26.649 0.000 16.000 18.702 2.211 17.106 19.391 o. 194 3.041 0.973 9.842 MSE Absolute % error 16.67% 32.26% 0.00% 23.53% 22.76% 9.91% 20.68% 20.02% 2.32% 8.30% 5.19% 14.70% MAPE ER. SANDEEP KUMAR 20
  21. Exponential Smoothing Exponential Smoothing 25 20 For 10 ER. SANDEEP KUMAR
  22. Trend & Seasonality Trend analysis technique that fits a trend equation (or curve) to a series of historical data points. projects the curve into the future for medium and long term forecasts. Seasonality analysis adjustment to time series data due to variations at certain periods. adjust with seasonal index — ratio of average value of the item in a season to the overall annual average value. example: demand for coal & fuel oil in winter months. ER. SANDEEP KUMAR 22
  23. Linear Trend Analysis Midwestern Manufacturing Sales Sales(in units) vs. Time Scatter Diagram Actual period value (or) number 74 79 80 90 105 142 122 (or) X 1995 1996 1997 1998 1999 2000 2001 160 140 120 IOO 80 60 40 20 0 1994 1996 1998 2000 2002 ER. SANDEEP KUMAR • Period number (or) X 23
  24. Least Squares for Linear Regression Midwestern Manufacturing Least Squares Method Time ER. SANDEEP KUMAR
  25. Least Squares Method Y=a+bX Where Y = predicted value of the dependent variable (demand) X = value of the independent variable (time) a = Y-axis intercept b = slope of the regression line ER. SANDEEP KUMAR [Exy Ex -nXY] 2 25
  26. Linear Trend Data & Error Analysis Midwestern Manufacturing Company Forecasting Input Data period Year I Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Intercept Slope Next period Linear trend analysis Actual value Period number Forecast Error Analysis Absolute errOr 6.750 1.214 8.321 8.857 4.393 22.071 8.464 8.582 MAD Squared Absolute 74 79 80 90 105 142 122 56.714 10.536 141 .ooo 1 2 3 4 5 6 7 8 Forecast 67.250 77.786 88.321 98.857 109.393 1 19.929 130.464 Average Error 6.750 1.214 -8.321 -8.857 -4.393 22.071 -8.464 error 45.563 I .474 69.246 78.449 19.297 487.148 71.644 110.403 MSE ER. SANDEEP KUMAR % error 9.12% I .540/0 10.40% 9.84% 4.18% 15.54% 6.94% 8.22% MAPE 26
  27. Least Squares Graph Trend Analysis 160 140 120 IOO 80 60 40 20 Time Actual v Linear (Actual values) ER. SANDEEP KUMAR
  28. Seasonality Analysis Ratio demand / average demand Eichler Supplies Year 1 2 Month Demand January February March April May June July August September October November December January February March April May June July August September October November December 80 75 80 90 115 110 100 90 85 75 75 80 100 85 90 110 131 120 110 110 95 85 85 80 Average Demand 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 Ratio 0.851 0.798 0.851 0.957 ? .223 1.170 ? .064 0.957 0.904 0.798 0.798 0.851 ? -064 0.904 0.957 1.170 ? .394 ? .277 1.170 1.170 1.011 0.904 0.904 0.851 Seasonal Index 0.957 0.851 0.904 ? .064 ? .309 ? .223 1.117 ? .064 0.957 0.851 0.851 0.851 Seasonal Index — ratio of the average value of the item in a season to the overall average annual value. Example: average of year 1 January ratio to year 2 January ratio. (0.851 + 1.064)/2 0.957 if Year 3 average monthly demand is expected to be 100 units. Forecast demand Year 3 January: 100 X 0.957 96 units Forecast demand Year 3 May: 100 X 1.309 131 units ER. SANDEEP KUMAR 28
  29. Deseasonalized Data • Going back to the conceptual model, solve for trend: Trend = Y / Season (96 units/ 0.957 = 100.31) This eliminates seasonal variation and isolates the trend Now use the Least Squares method to compute the Trend ER. SANDEEP KUMAR
  30. Forecast Now that we have the Seasonal Indices and Trend, we can reseasonalize the data and generate the forecast Y = Trend x Seasonal Index ER. SANDEEP KUMAR 30

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