Question

Ch8-A For data of weekly returns (in %) of Google stock given here, forecast the return for the week of March 5, 2017 as follows. [Note: Express your forecasts in % rounded to to 2 decimal places (eg, 3.23%), and express the MSE's and MAE rounded to 5 decimal places (e.g., 0.00073).] (a) Use a 3-week moving average and find the MSE and MAE. (b) Use exponential smoothing with alpha value 0.3 and compute the error measures (c) Now using a Data Table, perform exponential smoothing with alpha values: 0.1,0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. Choose the alpha with the smallest MSE What is the best forecast here and the corresponding alpha? (d) Which method is better between (a) 3-week mov. ave. and (c) expo smoothing with the best alpha? Show MSE's to support your answer. 14111242326 m02-0-4100-150-0-240-02-21100 6666666666667777777777 1123 1/-/2 /2 2/ 1 1 2 1 1/ 1 23 /1 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 225 26 27 28 29 30 31 32 33 35

Answer 1

(a)

3 - week moving average and MSE and MAE

3-week Squared Absolute Week of Return Moving AverageError 10-10-2016 | 0.45% 10/17/2016 | 2.68% 10/24/2016 | -0.50% 10/31/2016 | 4.19% 11-07-2016 | -1.05% 11/14/2016 | 0.86% 11/21/2016 | 0.15% 11/28/2016 | -1.47% 12-05-2016 | 5.17% 12-12-2016 | 0.19% 12/19/2016 | -0.11% 12/27/2016 | -2.29% 01-03-2017 | 4.45% 01-09-2017| 0.21% 1/17/2017 | -0.35% 1/23/2017 | 2.27% 1/30/2017 | -2.65% 02-06-2017| 1.62% 2/13/2017 | 1.77% 2/21/2017 | 0.07% 2/27/2017 | 0.80% 03-05-2017 Error Error 0.88% -0.67%| 1.91%, 1.46%) -0.01%| -0.15%| 1.28%| 1.30% 1.75%| -0.74%| 0.68%, 0.79% 1.44% 0.71%) -0.24%| 0.38%, 0.21%) 1.12% 0.88% 0.44% -1.38%) -3.52%) 0.86%) 2.32%) 0.16%| -1.32%) 3.89%| -1.11%) -1.86%| -1.55%) 3.77%) -0.58%) -1.79%) 1.56%) -2.41%) 1.14%) 1.56%) -1.05%) -0.08%) 0.02%) 0.12%) 0.01%) 0.05%) 0.00%| 0.02%) 0.15%| 0.01%) 0.03%| 0.02%) 0.14%) 0.00%) 0.03%) 0.02% 0.06%) 0.01%) 0.02% 0.01%) 0.00%) 1.38% 3.52% 0.86% 2.32% 0.16% 1.32% 3.89% 1.11% 1.86% 1.55% 3.77% 0.58% 1.79% 1.56% 2.41% 1.14% 1.56% 1.05% 0.08% 2 6 MSE МАЕ 1.67860%

(b)

Exponential smooting for alpha =0.3 and error measures

Exp Smoothing 0.3 Squared Absolute Week ofReturn 10-10-2016| 0.45% 10/17/2016 | 2 68% 10/24/201 6-0 .50% 10/31/2016 4.19% 11-07-2016 |-1.05% 11/14/2016 0.8 11/21/2016| 0.15% 11/28/20 16-147% 12-05-2016 517% 12-12-2016 019% 12/19/2016 -0.11% 12/27/2016|-2.29% 01-03-2017| 4.45% 01-09-2017| 0.21% 1/17/2017 |-0.35% 1/23/20172.27 1/30/2017 |-2.65% 02-06-2017| 1.52% 2/13/2017| 1.77% 2/21/2017 | 0.07% 2/27/2017 | 0.80% 03-05-2017 Error Error Error 0.45% 1.129 0.63% -0.81% -0.88% -0.36%) -0.21% -0.59%) 1.14% 0.86% 0.57% -0.29%) 1.13% 0.85% 0.49%) 1.03% -0.08%) 0.40%) 0.81% 0.59%) 0.65% 2.23%) -1.629 -4.82%| -0.24%) 1.74% 0.51%) -1.26%) 5.76%) -0.95%) -0.97%) -2.86%| 4.74% -0.92%) -1.20%) 1.78% -3.68%) 1.60%) 1.37%) -0.74%) 0.21%) 0.05%) 0.03%) 0.23%| 0.00%) 0.03%) 0.00% 0.02%) 0.33%) 0.01%) 0.01%) 0.08%| %) 0.01%, 0.01%) 0.03%) 0.14%) 0.03%) 0.02%) 0.01%, 0.00% 2.23% 1.62% 4.82% 0.24% 1.74% 0.51% 1.26% 5.76% 0.95% 0.97% 2.86% 4.74% 0.92% 1.20% 1.7 6% ) 8% % 1.60% 1.37% 0.74% 0.21% 3.68 MSE МАЕ 0.06338% 1.94535

(c)

Data Table

Data Table AlphaForecast MSE МАЕ 0.11 0.21 0.31 0.41 05 0.61 0.71 0.81 0.91 0.52%) 0.05292%11.72522% 0.61%) 0.05765%1.83937% 0.65%) 0.06270%1.95958% 0.68%) 0.06818%2.09786% 0.69%) 0.074209 12.24771% 0.70%) 0.08087%) 2.38312% 0.70%) 0.08833%2.50298% 0.71%)0.09675%) 2.62971 % 0.74%) 0.10632%) 2.73983%

(d)

Considering the MSE measure of 3 -week moving average (=0.03955) is better compared to the exponential smooting forecast MSE for any smoothing factor