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Variable of interest

Time Series Analysis. Variable of interest. Components of an Observation. Observed variable (O) = Systematic component (S) + Random component (R). Level (current deseasonalized ). Trend (growth or decline). Seasonality (predictable seasonal fluctuation).

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Variable of interest

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  1. Time Series Analysis Variable of interest Ardavan Asef-Vaziri

  2. Components of an Observation Observed variable (O) = Systematic component (S) + Random component (R) Level (current deseasonalized ) Trend (growth or decline) Seasonality (predictable seasonal fluctuation) • Systematic component: Expected value of the variable • Random component: The part of the forecast that deviates from the systematic component • Forecast error: difference between forecast and actual demand Ardavan Asef-Vaziri

  3. Naive Forecast F(t+1) = At At : Actual valued in period t F(t+1) : Forecast for period t+1 The naive forecast can also serve as an accuracy standard for other techniques. Ardavan Asef-Vaziri

  4. Moving Average Three period moving average in period 7 is the average of: MA73 = (A7+ A6+ A5 )/3 Ten period moving average in period t is the average of: MAt10 = (At+ At-1+ At-2 +At-3+ ….+ At-9 )/10 n period moving average in period t is the average of: MAtn = (At+ At-1+ At-2 +At-3+ ….+ At-n+1 )/n Forecast for period t+1 is equal to moving average for period t Ft+1 =MAtn Ardavan Asef-Vaziri

  5. 4-Period Moving Average at period 20, and 21 The Actual cost of a specific task type for periods 17-20 was 600, 700, 680, 720, respectively MA420 = (A20+A19+A18+A17)/4 MA420 = (720+680+700+600)/4 = 675 It was used as forecast for period 21. The actual values in period 21 is 800 MA421 = (A21+A20+A19+A18)/4 MA421 = (800+720+680+700)/4=725 MA421 = 675 +(800- 600) /4=725 MA421 = MA420 +(A21- A17)/4 Ardavan Asef-Vaziri

  6. AS n increases, we obtain a smoother curve Micro $oft Stock Ardavan Asef-Vaziri

  7. Exponential Smoothing Ardavan Asef-Vaziri

  8. Exponential Smoothing α=.2 1 100 100 2 100 3 110 t At Ft 150 Since I have no information for F2, I just enter A1 which is 100 A1  F2 F3 =(1-α)F2 + α A2 F3 =.8(100) + .2(150) F3 =80 + 30 = 110 F3 =(1-α)F2 + α A2 F2 & A2  F3 A1  F2 A1 & A2  F3 Ardavan Asef-Vaziri

  9. Exponential Smoothing α=.2 3 110 Exponential Smoothing Takes into account All pieces of actual data 1 100 100 2 150 100 4 112 t At Ft 120 F4 =(1-α)F3 + α A3 F4 =.8(110) + .2(120) F4 =88 + 24 = 112 A3 & F3  F4 F4 =(1-α)F3 + α A3 A1 & A2  F3 A1& A2 & A3  F4 Ardavan Asef-Vaziri

  10. Smoothing constant .2 .05 The smaller the value of α, the smoother the curve. Ardavan Asef-Vaziri

  11. Mean Absolute Deviation (MAD) The lower the MAD, The better the forecast MAD is also an estimates of the Standard Deviation of forecast s1.25MAD 10/15/2014 Ardavan Asef-Vaziri 11

  12. Mean Absolute Deviation (MAD) 10/15/2014 Ardavan Asef-Vaziri 12

  13. Tracking Signal Detecting non-randomness in errors can be done using Control Charts (UCL and LCL) Tracking Signal UCL Time LCL 10/15/2014 Ardavan Asef-Vaziri 13

  14. Tracking Signal Tracking Signal UCL Time LCL 10/15/2014 Ardavan Asef-Vaziri 14

  15. Other Measures of Forecast Error • Mean Square Error (MSE) • An estimate of the variance of the forecast error • Mean absolute percentage error (MAPE) Ardavan Asef-Vaziri

  16. Measures of Forecast Error (MAD) Ardavan Asef-Vaziri

  17. Measures of Forecast Error (MAR) Et = At/Ft-1 Ardavan Asef-Vaziri

  18. FourBasic Characteristics of Forecasts • Forecasts are rarely perfect because of randomness. • Beside the average, we also need a measure of variation, which is called standard deviation • Forecasts are more accurate for groups of items than for individuals. • Forecast accuracy decreases as the time horizon increases. I see that you willget an A this semester. Ardavan Asef-Vaziri

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