Monthly closing stock prices, adjusted for dividends, were obtained for Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The time series graph of these data is shown below. a. Below are the results of fitting a third-order autoregressive model, AR (3). Write out the model. Are the second and third lagged values significant? Explain.
Final Estimates of Parameters
Type Coef SE Coef T P
Lag 1 0.9247 0.1898 4.87 0.000
Lag 2 0.0429 0.2603 0.16 0.870
Lag 3 -0.0764 0.1959 -0.39 0.699
Constant 8.362 1.223 6.84 0.000
b. Below are the results of fitting a first-order autoregressive model, AR (1). Write out the model. Is this model typical for stock price data? Explain.
Final Estimates of Parameters
Type Coef SE Coef T P
Lag 1 0.9098 0.0969 9.39 0.000
Constant 6.835 1.207 5.67 0.000

Question

Monthly closing stock prices, adjusted for dividends, were obtained for Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The time series graph of these data is shown below.  a. Below are the results of fitting a third-order autoregressive model, AR (3). Write out the model. Are the second and third lagged values significant? Explain.
Final Estimates of Parameters
Type Coef SE Coef T P
Lag 1 0.9247 0.1898 4.87 0.000
Lag 2 0.0429 0.2603 0.16 0.870
Lag 3 -0.0764 0.1959 -0.39 0.699
Constant 8.362 1.223 6.84 0.000
b. Below are the results of fitting a first-order autoregressive model, AR (1). Write out the model. Is this model typical for stock price data? Explain.
Final Estimates of Parameters
Type Coef SE Coef T P
Lag 1 0.9098 0.0969 9.39 0.000
Constant 6.835 1.207 5.67 0.000

Quizplus · Accepted Answer

The Answer is Let Boeing stock price be dependent variable y.
a.

Let Boeing stock price be dependent variable y. a. = 8.362 + 0.9247yt-1 + 0.0429yt-2 - 0.0764yt-3 The second and third lagged values are not significant, as can be seen by their relatively large P-values (0.870 and 0.699, respectively). b. = 6.835 + 0.9098yt-1 With a relatively large Lag 1 coefficient, this is similar to what we find with stock price data. However, the values are monthly and not daily, so they are not as volatile and less likely to be a random walk. In addition, the estimated intercept is not close to zero.

= 8.362 + 0.9247yt-1 + 0.0429yt-2 - 0.0764yt-3
The second and third lagged values are not significant, as can be seen by their relatively large
P-values (0.870 and 0.699, respectively).
b.

= 6.835 + 0.9098yt-1
With a relatively large Lag 1 coefficient, this is similar to what we find with stock price data. However, the values are monthly and not daily, so they are not as volatile and less likely to be a random walk. In addition, the estimated intercept is not close to zero.

Monthly Closing Stock Prices, Adjusted for Dividends, Were Obtained for Boeing