1Time Series Decomposition &Exponential Smoothing
2Readings• Multiplicative Time Series Decomposition: Read “TimeSeries Forecasting”, Notes Abridged from OperationsManageme...
3Three Systems of Techniques forBusiness Forecasting• First forecasting model is cause-and-effect.• This model assumes a c...
4Three Systems of Techniques forBusiness Forecasting• Second is the time-series model• Data are projected forward based on...
5Three Systems of Techniques forBusiness Forecasting• Third is the judgmental model.• To produce a forecast without useful...
Time Series Decomposition• Multiplicative Decomposition: Y=T*S*C*R• Additive Decompostion: Y=T+S+C+R6
7WBSEDCL EnergySales DataApr 2004 – Mar2008
8WBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Jul...
9Multiplicative Model: Sales = T*S*C*RAdditive Model: Sales = T+S+C+RWBSEDCL Energy Sales (MU) - April 2004 to Nov 2007700...
10WBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Ju...
11Seasonal Index0.850.900.951.001.051.10Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
12Deseasonalized Data Apr 2004 - Nov 2007800.00850.00900.00950.001000.001050.001100.001150.00Apr-04Jul-04Oct-04Jan-05Apr-0...
13Cyclical Component (May 2004 - Oct 2007)0.9200.9400.9600.9801.0001.0201.0401.0601.080May-04Aug-04Nov-04Feb-05May-05Aug-0...
14Multiplicative Model: Sales = T*S*C*RAPE = Absolute Percentage ErrorMAPE= Mean Absolute Percentage Error
15Additive Model: Sales = T+S+C+RSales in current period =a1*time +(b1*Jan+ b2*Feb + … b12*Dec)+(c1*Sales last period) +Er...
16
17Additive Model: Sales = T+S+C+RSales = 2.83*Time+ [258.14(If Month is Jan) +238.02*(If Month is Feb) +290.90*(If Month i...
18Additive Model: Sales = T+S+C+R
19Moving Averages &Exponential Smoothing• Exponential Smoothing• Holt’s Exponential Smoothing• Holt-Winters Exponential Sm...
20Moving Averages for Forecasts
21Exponential Smoothing for Forecasts700.00800.00900.001000.001100.001200.001300.00Apr-05Jun-05Aug-05Oct-05Dec-05Feb-06Apr...
22In-sample Prediction Errorusing MA & EWS Methods
23Forecasting with Various Averages:Exponential Smoothing9-month Sales171921232527293133Jan Feb Mar Apr May June Jul Aug S...
24Forecasting with Various Averages:Exponential Smoothing0.8Month SalesAll Prev.PeriodaverageLastPeriodMovingAverage(3mont...
25Exponential Smoothing• A weighted moving average– Weights decline exponentially– Most recent observation weighted most• ...
26Exponential Smoothing• Weight (smoothing coefficient) is W– Range from 0 to 1– Smaller W gives better smoothing(smoothin...
27Exponential Smoothing: Method11 YE =,)1( 1−−+= iii EWWYE for i = 2, 3, 4, …Ei = weighted average of actual obs Yi and it...
28EWS or EMA Weights decline fast:w, w*(1-w), w*(1-w)^2, w*(1-w)^3, w*(1-w)^4, …0.1 0.2 0.5 0.8 0.9Weight= WWeight= WWeigh...
29
30Sales vs. Smoothed Sales• Fluctuations havebeen smoothed• NOTE: thesmoothed value inthis case isgenerally a littlelow, s...
31Exponential Smoothing for Trent Data
32Exponential Smoothing: Holt’s MethodInitial Values: L1 = Y1, T1 = 0******************Preliminary forecast of Y for next ...
33Exponential Smoothing: Holt WintersMethodInitial Values:St = Yt/Average(Y1:Ys),t=1,2,…,s,Ls = Ys/Ss,Ts = [Average(Ys+1:Y...
34Exponential Smoothing: Holt WintersMethod1. Preliminary forecast of deseasonalized Y for (t+1)Lt = a*(Yt /St-s) + (1-a)*...
Calculation35
36Forecast by Exponential Smoothing
37Comparing Forecasts by Various Methods
Exponential Moving Average(Special Type of EWS)38
Exponential Moving Average(special type of EWS)39for 20-Period EMA, 0.0952(approx) of currentperiod value is considered an...
Stock Market Data40
Stock Market Data41
Stock Market Data42
Stock Market Data43
Upcoming SlideShare
Loading in …5
×

Business forecasting decomposition & exponential smoothing - bhawani nandan prasad - it director

1,423 views

Published on

Published in: Business, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,423
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
Downloads
49
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Business forecasting decomposition & exponential smoothing - bhawani nandan prasad - it director

  1. 1. 1Time Series Decomposition &Exponential Smoothing
  2. 2. 2Readings• Multiplicative Time Series Decomposition: Read “TimeSeries Forecasting”, Notes Abridged from OperationsManagement by K N Dervitsiotis, McGraw Hill, 1981• Additive Time Series Decomposition: Notes on PPTSlides• Exponential Smoothing:– Chapter 3, Business Forecasting, 5th Ed, Wilson & Keating,Tata-McGrawHill;• “Marriot Rooms Forecasting” Case
  3. 3. 3Three Systems of Techniques forBusiness Forecasting• First forecasting model is cause-and-effect.• This model assumes a cause determines anoutcome.• Cause may be an investment in informationtechnology, and the effect is sales.• This model requires historical data not only ofeffect (say, sales), but also the “cause” (say,information technology expenditure).
  4. 4. 4Three Systems of Techniques forBusiness Forecasting• Second is the time-series model• Data are projected forward based on anestablished method like -- moving average, simpleaverage, exponential smoothing, decomposition,and Box-Jenkins.• This model assumes data patterns from therecent past will remain stable in future.
  5. 5. 5Three Systems of Techniques forBusiness Forecasting• Third is the judgmental model.• To produce a forecast without useful historicaldata (while projecting sales for a brand newproduct or when market conditions changemaking past data obsolete).• In absence of historical data, alternative datacollected from experts in the field (Delphimethod), prospective customers (ConjointAnalysis), trade groups, business partners, orother relevant source of information.
  6. 6. Time Series Decomposition• Multiplicative Decomposition: Y=T*S*C*R• Additive Decompostion: Y=T+S+C+R6
  7. 7. 7WBSEDCL EnergySales DataApr 2004 – Mar2008
  8. 8. 8WBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07End of Nov 2007: How to Predict Future Sales?? (for Dec 2007, …)
  9. 9. 9Multiplicative Model: Sales = T*S*C*RAdditive Model: Sales = T+S+C+RWBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07
  10. 10. 10WBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07
  11. 11. 11Seasonal Index0.850.900.951.001.051.10Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
  12. 12. 12Deseasonalized Data Apr 2004 - Nov 2007800.00850.00900.00950.001000.001050.001100.001150.00Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07
  13. 13. 13Cyclical Component (May 2004 - Oct 2007)0.9200.9400.9600.9801.0001.0201.0401.0601.080May-04Aug-04Nov-04Feb-05May-05Aug-05Nov-05Feb-06May-06Aug-06Nov-06Feb-07May-07Aug-07
  14. 14. 14Multiplicative Model: Sales = T*S*C*RAPE = Absolute Percentage ErrorMAPE= Mean Absolute Percentage Error
  15. 15. 15Additive Model: Sales = T+S+C+RSales in current period =a1*time +(b1*Jan+ b2*Feb + … b12*Dec)+(c1*Sales last period) +Error
  16. 16. 16
  17. 17. 17Additive Model: Sales = T+S+C+RSales = 2.83*Time+ [258.14(If Month is Jan) +238.02*(If Month is Feb) +290.90*(If Month is Mar) +161.15*(If Month is Apr) +309.87*(If Month is May) +271.00*(If Month is Jun) +335.06*(If Month is Jul) +291.76*(If Month is Aug) +309.07(If Month is Sep) +311.58*(If Month is Oct)+269.76*(If Month is Nov) +319.74*(If Month is Dec)]+ 0.64*(Prev Month Sale)
  18. 18. 18Additive Model: Sales = T+S+C+R
  19. 19. 19Moving Averages &Exponential Smoothing• Exponential Smoothing• Holt’s Exponential Smoothing• Holt-Winters Exponential Smoothing
  20. 20. 20Moving Averages for Forecasts
  21. 21. 21Exponential Smoothing for Forecasts700.00800.00900.001000.001100.001200.001300.00Apr-05Jun-05Aug-05Oct-05Dec-05Feb-06Apr-06Jun-06Aug-06Oct-06Dec-06Feb-07Apr-07Jun-07Aug-07Oct-07Energy Sales (MU)Simple EWSEWS HoltEWS Winters
  22. 22. 22In-sample Prediction Errorusing MA & EWS Methods
  23. 23. 23Forecasting with Various Averages:Exponential Smoothing9-month Sales171921232527293133Jan Feb Mar Apr May June Jul Aug SepMonthSales
  24. 24. 24Forecasting with Various Averages:Exponential Smoothing0.8Month SalesAll Prev.PeriodaverageLastPeriodMovingAverage(3month)ExponentialMovingAverage(w= )Jan 21Feb 23 21.00 21 21.00Mar 21 22.00 23 22.60Apr 20 21.67 21 21.67 21.32May 21 21.25 20 21.33 20.26June 19 21.20 21 20.67 20.85Jul 28 20.83 19 20.00 19.37Aug 32 21.86 28 22.67 26.27Sep 26 23.13 32 26.33 30.85Oct ?? 23.44 26 28.67 26.97
  25. 25. 25Exponential Smoothing• A weighted moving average– Weights decline exponentially– Most recent observation weighted most• Used for smoothing and forecasting(one period into the future)
  26. 26. 26Exponential Smoothing• Weight (smoothing coefficient) is W– Range from 0 to 1– Smaller W gives better smoothing(smoothing out unwanted cyclical and noisecomponents),– Larger W forecasts better(continued)
  27. 27. 27Exponential Smoothing: Method11 YE =,)1( 1−−+= iii EWWYE for i = 2, 3, 4, …Ei = weighted average of actual obs Yi and itsforecast Ei-1= forecast for next period (i+1)Weights: w, w*(1-w), w*(1-w)^2, w*(1-w)^3, w*(1-w)^4, …Yn, Yn-1, Yn-2, Yn-3, Yn-4, …
  28. 28. 28EWS or EMA Weights decline fast:w, w*(1-w), w*(1-w)^2, w*(1-w)^3, w*(1-w)^4, …0.1 0.2 0.5 0.8 0.9Weight= WWeight= WWeight= WWeight= WWeight= W0.100 0.200 0.500 0.800 0.9000.090 0.160 0.250 0.160 0.0900.081 0.128 0.125 0.032 0.0090.073 0.102 0.063 0.006 0.0010.066 0.082 0.031 0.001 0.0000.059 0.066 0.016 0.000 0.0000.053 0.052 0.008 0.000 0.0000.048 0.042 0.004 0.000 0.0000.043 0.034 0.002 0.000 0.0000.039 0.027 0.001 0.000 0.0000.035 0.021 0.000 0.000 0.000… … … … …Weight W = 0.50.0000.1000.2000.3000.4000.5000.6001 2 3 4 5 6 7 8 9 10 11Observation No.Weight
  29. 29. 29
  30. 30. 30Sales vs. Smoothed Sales• Fluctuations havebeen smoothed• NOTE: thesmoothed value inthis case isgenerally a littlelow, since thetrend is upwardsloping and theweighting factor isonly .201020304050601 2 3 4 5 6 7 8 9 10Time PeriodSalesSales Smoothed
  31. 31. 31Exponential Smoothing for Trent Data
  32. 32. 32Exponential Smoothing: Holt’s MethodInitial Values: L1 = Y1, T1 = 0******************Preliminary forecast of Y for next period (t+1):Lt = a*Yt + (1-a)*(Lt-1+Tt-1) for t = 2, 3, 4, …Correction Factor of “slope”:Tt = b*(Lt - Lt-1) + (1-b)*Tt-1 for t = 2, 3, 4, …Modified forecast of Y for next period (t+1):Ft = (Lt + Tt)
  33. 33. 33Exponential Smoothing: Holt WintersMethodInitial Values:St = Yt/Average(Y1:Ys),t=1,2,…,s,Ls = Ys/Ss,Ts = [Average(Ys+1:Y2s)– Average(Y1:Ys) ] /s
  34. 34. 34Exponential Smoothing: Holt WintersMethod1. Preliminary forecast of deseasonalized Y for (t+1)Lt = a*(Yt /St-s) + (1-a)*(Lt-1+Tt-1) for t = s+1, …2. Correction Factor of “slope” to add to preliminaryforecast of deseasonalized Y for (t+1) :Tt = b*(Lt - Lt-1) + (1-b)*Tt-1 for t = s+1, …3. Modified Forecast of deseasonalized Y for (t+1): (Lt + Tt)4. Correction Factor of “seasonality” (will be used speriods later) : St = c*(Yt /Lt) + (1-c)*St-s, t=s+1, …5. Final forecast of seasonal Y for (t+1):Ft = (Lt + Tt)*St+1-s
  35. 35. Calculation35
  36. 36. 36Forecast by Exponential Smoothing
  37. 37. 37Comparing Forecasts by Various Methods
  38. 38. Exponential Moving Average(Special Type of EWS)38
  39. 39. Exponential Moving Average(special type of EWS)39for 20-Period EMA, 0.0952(approx) of currentperiod value is considered and for 50-PeriodEMA, 0.0392(approx) of the current value isconsidered.Formula:EMA(current) = Price(current)x Multiplier +(1-Multiplier) x EMA(previous)Exact Weight or Multiplier= 2/(n+1)
  40. 40. Stock Market Data40
  41. 41. Stock Market Data41
  42. 42. Stock Market Data42
  43. 43. Stock Market Data43

×