Problem 15-05 (Algorithmic) Consider the following time Week 1 2 3 4 5 6 Value 1

ID: 369603 • Letter: P

Question

Problem 15-05 (Algorithmic) Consider the following time Week 1 2 3 4 5 6 Value 16 13 18 11 15 14 a. Choose the correct time series plot. series data. Time Series Value Time Series Value Weekit) Week(t tili) (w Time Series Value Time Series Value Week Weckt) What type of pattern exists in the data? b. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7, Round your answers alue 16 13 15 MSE: The forecast for week 7: c. Use -0.2 to compute the exponential smoothing values for the timc series, compute MSE and a forecast for week 7. two decimal places. 18 15 14 The forecast for week 7: d. Compare the three-week moving average forecast with the exponential smoothing forecast using -0.2, which appears to provide the better forecast based on MSE? The input in the box below will rot be graded, but may be reviewed and considered by your instructor

Explanation / Answer

Answer (a) - (ii) - Second graph is the correct answer

Beacuse the X-axis is 1,2,3,4,5,6 and the y-axis is 16,13,18,11,15,14, are plotted in correct order. Rest all the other three graphs do not have these values in order with respect to each other. So correct answer is (ii) option.

Pattern of data - The graph shows the pattern is fluctuating/ wave pattern i.e. inceasing then decreasing, then again increasing, again decreasing....the pattern is same i.e. changing the direction after every value. The overall pattern shows that the trend is decreaisng from 1st week to 6th week.

Answer (b) -

MSE - mean squared error is worked as below by calculating the forecast based on 3 weeks moving average method.

Week

T.S. value

3-Wk Moving Average

Forecast

Error

(Actual –Forecast)

Square of Error

=(16+13+18)/3

15.67

4.67

21.78

=(13+18+11)/3

14.00

-1.00

1.00

=(18+11+15)/3

14.67

0.67

0.44

Sum of error Square

23.22

Mean Squared Error (MSE) = Sum of Squared Error / No. of samples

Mean Squared Error (MSE) = 23.22 / 3

Mean Squared Error (MSE) = 7.74 ………..Answer

MSE = 7.74

Forecast for Week 7 = (11+15+14) / 3 = 13.33

Answer - c Exponential Smoothening Method of Forecasting

We can calculate forecast for the next week, if the forecast of the current week and actual value of current week is available with alpha value , as below

F t+1 (next week) = alpha * Actual (t) + (1-alpha) * Ft

Alpha = 0.2

Since the forecast value for any one of the week is not given in the question, so we can not calculate the forecast for week 7 and MSE for this problem.

Further answer can not be completed due to lack of information of forecast value for any of the week.