Business forecasting decomposition & exponential smoothing - bhawani nandan prasad - it director
1Time Series Decomposition &Exponential Smoothing
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
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).
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.
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.
Time Series Decomposition• Multiplicative Decomposition: Y=T*S*C*R• Additive Decompostion: Y=T+S+C+R6
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, …)
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
10WBSEDCL Energy Sales (MU) - April 2004 to Nov 200770075080085090095010001050110011501200Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07
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-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07
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
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)
25Exponential Smoothing• A weighted moving average– Weights decline exponentially– Most recent observation weighted most• Used for smoothing and forecasting(one period into the future)
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)
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, …
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)
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
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 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)