SECTION 13.3 Exercises

For Exercises 13.18 to 13.20, see pages 670–671; for 13.21 to 13.23, see page 677; for 13.24, see page 679.

Question 13.25

13.25 Existing home sales.

Each month, the National Association of Realtors releases a report on the number of existing home sales. The number of existing home sales measures the strength of the housing market and is an key leading indicator of future consumer purchases such as home furnishings and insurance services. Consider monthly data on the number of existing homes sold in the United States, beginning in January 2010 and ending in June 2014.16

hsales

  1. Use software to make a time plot of these data.
  2. Describe the overall trend present in these data.
  3. Do these data exhibit a regular, repeating pattern (seasonal variation)? If so, describe the repeating pattern.

13.25

(b) Overall, existing home sales are going up. (c) There is seasonal trend every year, with sales up between April and June and lows during January and February.

Question 13.26

13.26 Existing home sales.

Continue the previous exercise.

hsales

  1. Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.

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  2. Based on the fit, make a forecast for the number of existing homes sold for July 2014.
  3. Based on the regression output, which variables appear not to be contributing significantly to the fit? Rerun the regression without those variables and report your estimated model.

Question 13.27

13.27 Hotel occupancy rate.

A fundamental measure of the well-being of the hotel industry is the occupancy rate. Consider monthly data on the average hotal occupancy rate in the United States, beginning in January 2011 and ending in June 2014.17

hotel

  1. Use statistical software to make a time plot of these data.
  2. Does this time series exhibit a trend? If so, describe the trend.
  3. Do these data exhibit a regular, repeating pattern (seasonal variation)? If so, describe the repeating pattern.

13.27

(b) Overall, occupancy rates are going up slightly. (c) There is a seasonal trend every year, with rates peaking in June and July and lows during December and January.

Question 13.28

13.28 Hotel occupancy rate.

Continue the previous exercise.

hotel

  1. Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.
  2. Does the regression output suggest the presence of a trend? Explain how you reach your conclusion.
  3. Based on the fit, make a forecast for occupancy rate for July 2014.

Question 13.29

13.29 Hourly earnings.

Consider monthly data on the hourly earnings of production and nonsupervisory employees in private U.S. industry, beginning in January 2010 and ending in July 2014.18

earn

  1. Make a time plot of these data. Describe the overall movement of the data series.
  2. Does this time series exhibit a trend? If so, describe the trend.
  3. Do these data exhibit a regular, repeating pattern (seasonal variation)? If so, describe the repeating pattern.

13.29

(a) Earning is increasing over time. (b) Yes, there is a trend; earning is increasing over time. (c) It is hard to discern a seasonal pattern, though earning seems to be somewhat stable at times and then starts to climb rapidly during other times.

Question 13.30

13.30 Hourly earnings.

Continue the previous exercise.

earn

  1. Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to the data series. Report your estimated model.
  2. Does the regression output suggest the presence of seasonality? Explain how you reach your conclusion.
  3. Based on the regression output, which variables appear not to be contributing significantly to the fit? Rerun the regression without those variables and report your estimated model.
  4. Based on the fit from part (c), make a forecast for the occupancy rate for August 2014.

Question 13.31

13.31 Visitors to Canada.

Given the economic implications of tourism on regions, governments and many businesses are keenly interested in tourism at local and national levels. To promote and monitor tourism to Canada, the Canadian national government established the Canadian Travel Commission (CTC).19 One of the key indicators monitored by the CTC is the number of international visitors to Canada. In this exercise, you explore a data series on the number of monthly visitors to Canada from the United States and other countries. The data are monthly, starting with January 2009 and ending on May 2014.

visitca

  1. Make two time plots, one for the number of visitors from the United States and one for the number of visitors from other countries.
  2. In both cases, for what months is visitation highest? During the off-season period, what particular month shows a bit of a surge?
  3. Do there appear to be trends in the two series? Explain.

13.31

(b) Visitation is highest in July. In the off-season there is a surge in December. (c) There doesn’t appear to be a trend for the US; for the NonUS there is maybe a very slight upward trend.

Question 13.32

13.32 Visitors to Canada.

Continue the previous exercise.

visitca

  1. Make indicator variables for the months of the year, and fit a linear trend along with 11 indicators to each of the two data series. Report your estimated models.
  2. Based on these fits, make forecasts for the number of visitors from the United States and the number of visitors from countries other than the United States for June 2014.
  3. Based on the regression outputs, which variables appear to not be contributing significantly to the fit? Rerun the regressions without those variables and report your estimated models.

Question 13.33

13.33 AT&T wireline business.

With the continuing growth of the wireless phone market, it is interesting to study the impact on the wireline (landline) phone market. Consider a time series of the quarterly number of AT&T customers (in thousands) who have wireline voice connections.20 The series begins with the fourth quarter of 2011 and ends with the second quarter of 2014.

att

  1. Make a time plot of these data. Describe the overall movement of the data series.
  2. Does there appear to be seasonality?
  3. Fit the time series with a linear trend model. Report the estimated model.
  4. Superimpose the fitted linear trend model on the data series. Does the fit seem adequate? If not, explain why not.

13.33

(a) The number of wireline voice connections has been steadily decreasing over this time period. (b) There is no seasonal pattern. (c) . (d) The data appear to curve rather than follow a straight line.

Question 13.34

13.34 AT&T wireline business.

Continue the previous exercise.

att

  1. Based on the estimated linear trend model from part (c) of Exercise 13.33, obtain the residuals and plot them as a time series. Describe the pattern in the residuals.

    681

  2. Now consider a quadratic trend model. Fit a regression model based on two explanatory variables: and where . Report the estimated model.
  3. Based on the estimated quadratic trend model, compute the residuals and plot them as a time series. Is there a pattern in the residuals?
  4. Superimpose the fitted quadratic trend model on the data series. Explain in what way the quadratic fit is an improvement over the linear trend fit of Exercise 13.33.

Question 13.35

13.35 Runs test and autocorrelation.

Suppose you have three different time series S1, S2, and S3. The observed number of runs for series S1 is significantly less than the expected number of runs. The observed number of runs for series S2 is significantly greater than the expected number of runs. The observed number of runs for series S3 is not significantly different from the expected number of runs. If you were to plot observations of a given series against its first lag, explain what you would likely see.

13.35

S1 would show a strong positive relationship with its first lag, S2 would show a strong negative relationship with its first lag, and S3 would show no particular relationship with its first lag.

Question 13.36

13.36 Monthly warehouse club and superstore sales.

Consider the monthly warehouse club and superstore sales series discussed in Examples 13.15 and 13.16 (pages 671–674).

club

  1. Fit the trend-seasonal model shown in Example 13.16 and obtain the residuals from the fitted model. Plot the residuals as a time series. Describe the pattern in the residuals. Upon closer inspection, is this pattern evident in the time plot of the sales series shown in Figure 13.28 (page 672)? Explain.
  2. Now consider adding a quadratic trend term to the model. Fit a regression model based on , and the 11 seasonal variables. Is the quadratic term significant?
  3. Based on the estimated model of part (b), obtain the residuals and plot them as a time series. Is there a pattern in these residuals?
  4. Provide a forecast for sales for June 2014.

Question 13.37

13.37 A more compact model.

Suppose you fit a trend-and-seasonal model to a time series of quarterly sales and you find the following:

Reexpress this fitted model in a more compact form using only one indicator variable.

13.37

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