Answer (a) – The correct time plot is option ( iii ). The graph is made with bel
ID: 373376 • Letter: A
Question
Answer (a) – The correct time plot is option ( iii ).
The graph is made with below headings
Pattern in the data
The pattern in the time series value/data is fluctuating i.e. increases, then decreases, again increase and then again decreases. But if we see overall trend, the data is in decrease pattern. If we plot the trend line for the data, the trend line will be declined line with advancement of weeks, it indicates the with weeks advancement, the time series value decreases.
Answer (b)
Three week moving average for the table is as below.
Week
T.S. value
3-Wk Moving Average
Forecast
Error
(Actual –Forecast)
Square of Error
1
19
2
14
3
17
4
12
=(19+14+17)/3
16.67
- 4.67
21.81
5
17
=(14+17+12)/3
14.33
2.67
7.13
6
14
=(17+12+17)/3
15.33
-1.33
1.77
7
= (12+17+14)/3
14.33
Sum of error Square
30.71
Mean Squared Error (MSE) = Sum of Squared Error / No. of samples
Mean Squared Error (MSE) = 30.71 / 3
Mean Squared Error (MSE) = 10.235 = 10.24 ………..Answer
Forecast for week 7 = 14.33
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 cannot calculate the forecast for week 7 and MSE for this problem.
Further answer (d) and (e) cannot be completed due to lack of information of forecast value for any of the week.
Week
T.S. value
3-Wk Moving Average
Forecast
Error
(Actual –Forecast)
Square of Error
1
19
2
14
3
17
4
12
=(19+14+17)/3
16.67
- 4.67
21.81
5
17
=(14+17+12)/3
14.33
2.67
7.13
6
14
=(17+12+17)/3
15.33
-1.33
1.77
7
= (12+17+14)/3
14.33
Sum of error Square
30.71
Explanation / Answer
Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 19 14 17 12 17 14 a. Choose the correct time series plot. 20r Time Series Value Time Series Value 16 12 10 Week(t) Week(t) (iv) 20r Time Series Value Time Series Value 18 10 Week(t) Week(t) What type of pattern exists in the data?