1. 4/16/2015 1 Ardavan Asef-Vaziri Variable of interest Time Series Analysis

2. Components of an Observation 4/16/2015Ardavan Asef-Vaziri 2 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

3. A t : Actual valued in period t F (t+1) : Forecast for period t+1 F (t+1) = A t Naive Forecast The naive forecast can also serve as an accuracy standard for other techniques. 4/16/2015 3 Ardavan Asef-Vaziri

4. Moving Average Three period moving average in period 7 is the average of: MA 7 3 = (A 7 + A 6 + A 5 )/3 4/16/2015 4 Ardavan Asef-Vaziri MA t 10 = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-9 )/10 Ten period moving average in period t is the average of: n period moving average in period t is the average of: MA t n = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-n+1 )/n Forecast for period t+1 is equal to moving average for period t F t+1 =MA t n

5. MA 4 21 = (A21+A20+A19+A18)/4 MA 4 21 = (800+720+680+700)/4=725 4-Period Moving Average at period 20, and 21 It was used as forecast for period 21. The actual values in period 21 is 800 The Actual cost of a specific task type for periods 17-20 was 600, 700, 680, 720, respectively 4/16/2015 5 Ardavan Asef-Vaziri MA 4 20 = (A20+A19+A18+A17)/4 MA 4 20 = (720+680+700+600)/4 = 675 MA 4 21 = MA 4 20 +(A21- A17)/4 MA 4 21 = 675 +(800- 600) /4=725

6. Micro $oft Stock 4/16/2015 6 Ardavan Asef-Vaziri AS n increases, we obtain a smoother curve

7. Exponential Smoothing 4/16/2015 7 Ardavan Asef-Vaziri

8. Exponential Smoothing α=.2 t At Ft 1 100 A1  F2 2 100 Since I have no information for F2, I just enter A1 which is 100 150 F3 =(1-α)F2 + α A2 F3 =.8(100) +.2(150) F3 =80 + 30 = 110 3 110 F2 & A2  F3 A1  F2A1 & A2  F3 F3 =(1-α)F2 + α A2 4/16/2015 8 Ardavan Asef-Vaziri

9. Exponential Smoothing α=.2 t At Ft 1 100 F4 =(1-α)F3 + α A3 F4 =.8(110) +.2(120) F4 =88 + 24 = 112 A3 & F3  F4 A1 & A2  F3A1& A2 & A3  F4 2 150 100 3 110 4 112 120 F4 =(1-α)F3 + α A3 Exponential Smoothing Takes into account All pieces of actual data 4/16/2015 9 Ardavan Asef-Vaziri

10. .2 .05 Smoothing constant The smaller the value of α, the smoother the curve. 4/16/2015 10 Ardavan Asef-Vaziri

11. Mean Absolute Deviation (MAD) 4/16/2015 11 Ardavan Asef-Vaziri The lower the MAD, The better the forecast MAD is also an estimates of the Standard Deviation of forecast   1.25MAD

12. Mean Absolute Deviation (MAD) 4/16/2015 12 Ardavan Asef-Vaziri

13. Tracking Signal UCL LCL Time Detecting non-randomness in errors can be done using Control Charts (UCL and LCL) 4/16/2015 13 Ardavan Asef-Vaziri

14. Tracking Signal UCL LCL Time Tracking Signal 4/16/2015 14 Ardavan Asef-Vaziri

15. 4/16/2015Ardavan Asef-Vaziri 15 Other Measures of Forecast Error  Mean Square Error (MSE)  An estimate of the variance of the forecast error  Mean absolute percentage error (MAPE)

16. 4/16/2015Ardavan Asef-Vaziri 16 Measures of Forecast Error

17. 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 will get an A this semester. Four Basic Characteristics of Forecasts 4/16/2015 17 Ardavan Asef-Vaziri