What do we mean by the term “autocorrelation”? Describe the impact of autocorrelation on estimation

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

PART A   

 1. Consider the following CNLRM:

i = 1, 2, …, 5

 and the following data:

                                    X                       Y

                                    4                        8

                                   6                      14

                                   2                        6

                                 10                      18

                                 18                      34

 i) Compute the ordinary least squares estimates of the and parameters.

ii) Compute .

iii) Compute .

iv) Compute adjusted-.

v) Construct a two-sided 95% confidence interval for .

vi) Test the null hypothesis  against the alternative hypothesis  at the 5% significance level.

  2. Consider the intercept-only CNLRM: 

 i = 1, 2, …, n 

where ~ N.

i) Derive the least squares estimator of .

ii) Prove that this least squares estimator is (a) linear and (b) unbiased.

iii) Derive the variance of this least squares estimator.

iv) Write down the appropriate unbiased estimator of that would be used with this model for regular econometric inference.

v) Derive the maximum likelihood estimators of and. (NOTE: You do NOT need to check the second-order condition.) 

3. Discuss the Chow Test and the MWD Test. Be sure to include the following elements in your discussion: 

i) Purpose

ii) Detailed instructions as to practical implementation

iii) Interpretation of results

iv) Implications of results for further econometric investigation 

(NOTE: You MAY wish to include a SHAZAM sub-program as a part of your answer to part ii).) 

PART B    

4. One day you happen to overhear part of a conversation between two graduate students in the Loeb Cafeteria. The first student claims that “Multicollinearity is no big deal. I really don’t know what all the fuss is about. After all, you can always just drop a variable or two, find some more data, or, if absolutely necessary, use ridge regression.” The second student is speechless. What do you think? Explain.   

5. What do we mean by the term “autocorrelation”? Describe the impact of autocorrelation on estimation and inference within the context of the CNLRM. How can we detect the presence of autocorrelation? Should anything be done about autocorrelation if it is detected? If so, what should be done? Be specific. If not, why not?

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