2015 01 28

CCN2266 In-class exercise 1 solution

Question 1

The following data gives the daily closing values of a stock over the past 8 days. a) Use a centered three-day moving average to smooth the given data. b) Use a centered five-day moving average to smooth the given data. c) Use a 3-day moving average to forecast the daily closing values of the stock from the 4th day to the 9th day. d) Use a 5-day moving average to forecast the daily closing values of the stock from the 6th day to the 9th day.

Day Values centered 3-day

MA centered 5- day MA

3-day MA forecast

5-day MA forecast

1 1555 2 1688 1601.00 3 1560 1641.67 1634.60 4 1677 1643.33 1655.00 1601.00 5 1693 1675.67 1669.20 1641.67 6 1657 1703.00 1717.20 1643.33 1634.60

7 1759 1738.67 1675.67 1655.00 8 1800 1703.00 1669.20 9 1738.67 1717.20

Question 2

The following table provides the weekly profit (in $1,000) of a trading company for the past 6 weeks. Use a centered four-week moving average to smooth the data.

Week Values 4-week MA 4-week centered MA

1 117.8 2 125.1 120.95 3 110.9 122.85 124.75 4 130.0 124.33 123.90 5 133.0 6 121.7

Question 3

a) Name the four time series components.

Trend component

Seasonal component

Cyclical component

Irregular component

b) State the assumption of continuity in the context of quantitative forecasting methods. Assume the past pattern of the time series data will continue into the future.

2015 01 28

Question 4

The monthly operational cost, Y (in $1,000), of a well-known fast food shop for the past 6 months are listed in the table below. Use exponential smoothing with a smoothing constant of 0.3 to smooth the costs.

Month Y

(in $1,000) Exponentially smoothed value

(in $1,000)

1 324 324

2 472 368.40

3 310 350.88

4 351 350.92

5 378 359.04

6 432 380.93

Question 5

The following data gives the weekly sales of company ABC over a 5-week period.

Week 1 2 3 4 5

Weekly sales 410 461 422 488 439

a) Use a centered three-week moving average to smooth the given weekly sales. b) Use exponential smoothing with smoothing constant 0.4 to forecast the weekly sales from week 2 to week 5.

a

Week Weekly sales

Centered 3-week MA

1 410

2 461 00.431

3 422 457.00

4 488 449.67

5 439

b

Week Weekly sales Weekly forecasts

1 410

2 461 410.00

3 422 40.430

4 488 427.04

5 439 451.42

Question 6

A sales manager forecast each weeks sales by exponential smoothing with smoothing constant 0.8. Suppose the forecast of sales for last week was $28,123. But the actual sales last week turned out to be $37,100. Calculate the sales forecast for this week.

( ) ( )( ) 6.304,35$281238013710080 = . + .

Question 7

In general for a time series of N periods, how many centered moving averages with a chosen period of length n

can be constructed for smoothing the given time series? Assume Nn and n is odd.

You may use ( ) 11 += nNnN

or simply give 1+ nN