Time series analysis 26 The quarterly sales data number of c

Time series analysis

26. The quarterly sales data (number of copies sold) for a college textbook over the past

       three years follows.

            Quarters                      Years 1            Years 2            Year 3

            1                                1690                1800                1850

            2                                  940               900                1100

             3                                 2625                2900                2930

           4                                 2500                2350                2615

a. Construct a time series plot. What type of pattern exists in the data?

b. Use a regression model with dummy variables as follows to develop an equation to

     account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1

                  if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.

c. Compute the quarterly forecasts for next year.

d. Let = 1torefertotheobservationinquarter1ofyear1; t=2 to refer to the

   observation in quarter 2 of year 1; . . . ; and t =12 to refer to the observation in quarter

    4 of year 3. Using the dummy variables defined in part (b) and also using t; develop an

    equation to account for seasonal effects and any linear trend in the time series. Based

    upon the seasonal effects in the data and linear trend, compute the quarterly forecasts

    for next year.

27. Air pollution control specialists in southern California monitor the amount of ozone, carbon

    dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data

      exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours

      in the day. On July 15, 16, and 17, the following levels of nitrogen dioxide were observed for

       the 12 hours from 6:00 A.M. to 6:00 P.M.

July15: 25 28 35 50 60 60 40 35 30 25 25 20

            July16: 28 30 35 48 60 65 50 40 35 25 20

July17: 35 42 45 70 72 75 60 45 40 25 25 25

Construct a time series plot. What type of pattern exists in the data?

Use a multiple linear regression model with dummy variables as follows to develop

an equation to account for seasonal effects in the data:

Hour1 = 1 if the reading was made between 6:00 A.M. and 7:00 A.M.; 0 otherwise

Hour2 = 1 if the reading was made between 7:00 A.M. and 8:00 A.M.; 0 otherwise.

Hour11 = 1 if the reading was made between 4:00 P.M. and 5:00 P.M.; 0 otherwise

Note that when the values of the 11 dummy variables are equal to 0, the observation

corresponds to the 5:00 P.M. to 6:00 P.M. hour.

Using the equation developed in part (b), compute estimates of the levels of

Nitrogen dioxide for July 18.

Let t = 1 to refer to the observation in hour 1 on July 15; t = 2 to refer to the

observation in hour 2 of July 15…... and t = 36 to refer to the observation in hour 12 of July 17. Using the dummy variables defined in part (b) and t, developing an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18.

Solution