SECTION 13.4 Exercises

691

For Exercises 13.38 and 13.39, see page 690.

Question 13.40

13.40 MLB batting average.

Consider data on the annual average batting average of all Major League Baseball (MLB) teams of a given year. The data series begins with 1960 and ends with 2013.24

mlb

  1. Make a time plot of the batting average series. Describe any important features of the time series.
  2. Create a lag one variable and plot the batting average of a given year against its lag. Does the plot suggest the use of the lag variable as a possible predictor variable? Explain.
  3. If your software has the option, obtain a PACF for the batting average series. What does the PACF suggest as a possible model to fit to the data?

Question 13.41

13.41 Amazon sales.

CASE 13.1 In Example 13.25, the one-step ahead forecast was calculated. Using the model of Example 13.25, determine the two-step ahead forecast in original dollar units.

13.41

. Undoing the transformation yields .

Question 13.42

13.42 MLB batting average.

Continue the analysis of MLB batting averages from Exercise 13.40.

mlb

  1. Use software to fit a simple linear regression model, using as the response variable and as the explanatory variable. Record the estimated regression equation.
  2. Obtain the residuals from the AR(1) fit and make a time series plot of the residuals. Do the residuals appear random?
  3. Test the residuals for randomness with an ACF. Does it appear that the autocorrelation has been accounted for? Explain.
  4. Use the fitted AR(1) model from part (a) to obtain forecasts for batting averages in 2014 and 2015.

Question 13.43

13.43 OPEC basket prices.

In 2005, OPEC introduced a basket price which is the average price of seven blends from different OPEC countries. OPEC uses the basket price to monitor world oil market conditions. Consider data on the daily basket price from the beginning of January 2012 to the middle of August 2014.25

opec

  1. Make a time plot of the price series. Describe any important features of the time series.
  2. Obtain the first differences for the series and test them for randomness. What do you conclude?
  3. Would you conclude that the price series behaves as a random walk? Explain.

13.43

(a) There is no consistent trend or seasonal pattern, but there are short runs where the value rises and falls. (b) The ACF shows the first differences of the price series are not random. (c) The first differences in a random walk are random; because the first differences for price are not random, it is unlikely the price series behaves like a random walk.

Question 13.44

13.44 OPEC basket prices.

Continue the previous exercise.

opec

  1. Obtain a PACF for the OPEC price series. How many lags does the PACF suggest should be considered in building a lag-based model?
  2. Based on your results from part (a), fit an appropriate lag model and report it.
  3. Obtain the residuals from the model fit in part (b) and test the residuals for randomness. What do you conclude?
  4. The last price in the series is for August 13, 2014. Based on the fitted model, what are the forecasts for August 14 and August 15?

Question 13.45

13.45 Warehouse club and superstore sales.

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

club

  1. Make scatterplot of sales versus (a lag of 12 periods). What does the scatterplot suggest?
  2. What is the correlation between and ?
  3. How well do sales 12 months ago appear to predict this month’s sales? Explain your response.

13.45

(a) Sales is linearly related to lag12sales. (b) . (c) . There is a significant linear relationship between this month’s sales and sales 12 months ago.