TIME SERIES and FORECASTING (Chapter 18)

Time Series p.1

FORECASTING SALES OF MOSQUITO REPELLENT

#1 #2 #3 #4 #5 #6 #7 #8 #9 Original 4-Quarter 4-Quarter Seasonal Seasonal De- De- Prediction Irregular Data Moving Centered Irregular Index Seasonal- Seasonal- #7x#5/100 #1/#8 x 100 Average Moving Value (Adjusted ized ized (quarters) Average #1/#3 X median ) Data Trend 100 (#1/Index)

2001 21 73.3 28.6 30.7 22.5 93.3 42 33.75(1-4) 127.6 32.9 34.7 44.3 94.8 60 37.25(2-5) 35.50 169.01 166.0 36.1 38.6 64.1 93.6 12 38.75 30.97 33.1 36.3 42.6 14.1 85.1

2002 40.25(3-6) 44.12 79.33 102.6 35 48.00(4-7) 47.7 46.5 34.1 54 48.25 111.92 42.3 50.4 64.3 84.0 48.50(5-8) 49.00 185.71 100.8 91 49.50(6-9) 54.8 54.4 90.3 14 53.00 26.42 42.3 58.3 19.3 72.5

2003 56.5(7-10) 59.75 65.27 85.4 39 63.00(8-11) 53.2 62.3 45.7 82 66.00 124.24 64.3 66.2 84.5 97.0 69.00(9-12) 73.88 158.36 100.5 117 78.75(10-13) 70.5 70.1 116.4 38 86.75 43.80 114.8 74.1 24.5 155.1

2004 94.75(11-14) 97.12 80.31 136.4 78 99.50(12-15) 106.4 78..0 57.2 146 98.50 148.22 114.4 82.0 104.6 139.6 97.5(13-16) 94.50 143.92 95.4 136 91.50(14-17) 81.9 85.9 142.6 30 87.50 34.29 90.6 89.8 29.8 101.0 83.50(15-18) 2005 54 86.50 62.43 73.7 93.8 68.8 78.5 89.50(16-19) 91.4 114 89.25(17-20) 89.38 127.55 89.3 97.7 124.7 160 96.4 101.7 168.8 94.8 29 97.6 105.6 35.0 82.9 Medians of Column #4 Trend with winter 2001 = period one Trend of Deseasonalized Q1 72.30 linear, y = 28.6 + 3.71t, r2 = .231 y = 26.8 + 3.94t, r2 = .682 Q2 125.90 quadratic, y = 12.2 + 8.2t - .214t2, r2 = .251 Q3 163.68 exponential, In y = 3.36 + .0578t, r2 = .203 Q4 32.63 y = 28.79(1.059)t 394.51 Time Series p.2 FORECASTING VACANCIES AT CASTLE POINT YEAR Vacancies 1 2 2 3 3 4 4 5 5 6 6 Forecast Error2 Forecast Error2 Forecast Error2 Forecast Error2 Forecast Error2

1996 59 54 25

1997 46 59 169 62 256 70 576

1998 64 56 50 196 71 49 59 25

1999 95 68 56 1521 57 1444 60 1225 79 256 75 400

2000 92 84 68 576 77 225 84 64 87 25 101 81

2001 95 94 84 121 88 49 90 25 96 1 98 9

2002 108 98 94 196 94 196 94 196 104 16 101 49

2003 110 104 98 144 101 81 104 36 112 4 112 4

2004 125 114 104 441 107 324 108 289 121 16 114 121

2005 121 119 114 49 117 16 120 1 129 64 126 25

Sum of Squared Errors 3048 2335 2201 712 1290

Mean Square Error 435 334 245 71 143

1. 3 point moving average to smooth 5. Linear trend with 1996 as period one Yt = 45.4 + 8.38t 2. Forecasting by M.A. (3 point) 6. Autoregression (one period)

3. Weighted (1,2,3) moving average forecast Yt = (20.1 + .850 Yt-1) 4. Exponential smoothing with  = 0.7