The following table reports the percentages of stocks in a typical portfolio in

Question

The following table reports the percentages of stocks in a typical portfolio in nine quarters from 2005 to 2007.

                  Quarter                               Stock %

                 1st-2005                                  29.8

                 2nd-2005                                 31.0

                 3rd-2005                                  29.9

                 4th-2005                                  30.1

                 1st-2006                                  32.2

                 2nd-2006                                 31.5

                 3rd-2006                                  32.0

                 4th-2006                                  31.9

                 1st-2007                                  30.0

A. use exponential smoothing to forecast this time series. Consider smoothing constants of a=.2, .3, and .4. What value of the smoothing constant provides the best forcast?

Explanation / Answer

We see that the mean squared error is least for alpha=0.2. Hence alpha=0.2 gives the best forecast.

Simple Exponential Smoothing Alpha .20 t Data Smoothed Forecast % error 30.75 * 1 29.8 30.56 30.8 -3.4 2 31.0 30.65 30.6 1.3 3 29.9 30.50 30.6 -2.3 4 30.1 30.42 30.5 -1.3 5 32.2 30.77 30.4 5.6 6 31.5 30.92 30.8 2.2 7 32.0 31.14 30.9 3.4 8 31.9 31.29 31.1 2.5 9 30.0 31.03 31.3 -4.3 31.0 1.01 Mean Squared Error 2.9% Mean Absolute Percent Error 55.6% Percent Positive Errors * initial value - mean of first six data values Simple Exponential Smoothing Alpha .30 t Data Smoothed Forecast % error 30.75 * 1 29.8 30.47 30.8 -3.4 2 31.0 30.63 30.5 1.6 3 29.9 30.41 30.6 -2.3 4 30.1 30.32 30.4 -1.0 5 32.2 30.88 30.3 5.9 6 31.5 31.07 30.9 1.9 7 32.0 31.35 31.1 2.8 8 31.9 31.51 31.3 1.9 9 30.0 31.06 31.5 -5.0 31.1 1.02 Mean Squared Error 2.9% Mean Absolute Percent Error 55.6% Percent Positive Errors * initial value - mean of first six data values Simple Exponential Smoothing Alpha .40 t Data Smoothed Forecast % error 30.75 * 1 29.8 30.37 30.8 -3.4 2 31.0 30.62 30.4 1.9 3 29.9 30.33 30.6 -2.3 4 30.1 30.24 30.3 -0.7 5 32.2 31.02 30.2 6.2 6 31.5 31.21 31.0 1.6 7 32.0 31.53 31.2 2.5 8 31.9 31.68 31.5 1.3 9 30.0 31.01 31.7 -5.7 31.0 1.09 Mean Squared Error 2.8% Mean Absolute Percent Error 55.6% Percent Positive Errors * initial value - mean of first six data values

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.