you estimate the following time-series regression:

Equation 1: yt=+xt+et

where, yt is the dependent variable, xt is the single regressor, and et is the shock.

[1 point] A) Is it innocuous to assume that the shocks are assumed to be mean zero? Explain your answer.

[3 points] B) Describe a test that could be used to assess whether there is serial correlation up to order 5 in the shocks.

• What is the null and the alternative hypothesis for the test?
• What distribution would you use for the test, if you had a large sample?
• State the decision rule you would use at the 5% level of significance.

You find evidence serial correlation and adjust the regression specification to include a first lag of the dependent variable:

Equation 2: yt=+xt+yt1+et

Applying the same test for serial correlation to this new linear regression model, you find evidence of remaining serial correlation at the 5% level of significance.

[2 points] C) . Would it be appropriate to use OLS estimates to conduct inference about the coefficients of the model in equation 2 using a sample of 15 observations? Explain your answer.

[2 points] D) Would it be appropriate to use OLS estimates to conduct inference about the coefficients of the model in equation 2 using a sample of 500 observations? Explain your answer.

[2 points] E) Suggest a modification to the linear regression model in equation 2 to address any concerns raised in parts C or D.