Deck 12: Serial Correlation and Heteroskedasticity in Time Series Regressions

Question 1

Which of the following is an example of FGLS estimation?

A)Dickey-Fuller estimation
B)Vector error correction estimation
C) Prais-Winsten estimation
D) OLS estimation.

Answer 1

C
Explanation: Prais-Winsten estimation is a type of FGLS estimation.

Question 2

Which of the following identifies an advantage of first differencing a time-series?

A)First differencing eliminates most of the serial correlation.
B)First differencing eliminates most of the heteroskedastcicty.
C) First differencing eliminates most of the multicollinearity.
D) First differencing eliminates the possibility of spurious regression.

Answer 2

A
Explanation: First differencing of a time-series helps eliminate most of the serial correlation.

Question 3

Which of the following is a test for serial correlation in the error terms?

A)Johansen test
B)Dickey Fuller test
C) Durbin Watson test
D) White test

Answer 3

C
Explanation: The Durbin Watson test can be used to test for serial correlation in error terms.

Question 4

A smaller standard error means:​

A)​a larger t statistic.
B)​a smaller t statistic.
C) ​a larger F statistic.
D) ​a smaller F statistic.

Question 5

Which of the following is the reason why standard errors measured by OLS differ from standard errors measured through Prais-Winsten transformation?

A)OLS standard errors account for serial correlation, whereas Prais-Winsten estimations do not.
B)Prais-Winsten standard errors account for serial correlation, whereas OLS estimations do not.
C) Prais-Winsten standard errors account for heteroskedasticity, whereas OLS estimations do not.
D) OLS standard errors account for heteroskedasticity, whereas Prais-Winsten estimations do not.

Question 6

Durbin's alternative test is valid even if the explanatory variables are strictly exogenous.

Question 7

For a given significance level, if the calculated value of the Durbin Watson statistic lies between the lower critical value and the upper critical value, _____.

A)the hypothesis of no serial correlation is accepted
B)the hypothesis of no serial correlation is rejected
C) the test is inconclusive
D) the hypothesis of heteroskedasticity is accepted

Question 8

When a series is stationary, weakly dependent, and has serial correlation:

A)the adjusted R² is inconsistent, while R² is a consistent estimator of the population parameter.
B)the adjusted R² is consistent, while R² is an inconsistent estimator of the population parameter.
C) both the adjusted R² and R² are inconsistent estimators of the population parameter.
D) both the adjusted R² and R² are consistent estimators of the population parameter.

Question 9

​In the time series literature, the serial correlation-robust standard errors are sometimes called:

A)​homoskedasticity and autocorrelation inconsistent standard errors.
B)​homoskedasticity and autocorrelation consistent standard errors.
C) ​heteroskedasticity and autocorrelation inconsistent standard errors.
D) ​heteroskedasticity and autocorrelation consistent standard errors.

Question 10

The equation u²t = ₀ + ₁u²t _{- 1} + v_t is an autoregressive model in _____.

A)u_t
B)u²t
C) v_t
D) u_{t - 1}

Question 11

In the presence of heteroskedasticity, the usual OLS estimates of:

A)standard errors are valid, whereas the t statistics and F statistics are invalid.
B)t statistics are valid, but the standard errors and F statistics are invalid.
C) F statistics are valid, but the standard errors and t statistics are invalid.
D) standard errors, t statistics, and F statistics are invalid.

Question 12

Consistency of FGLS requires:

A)​u_t to be uncorrelated with x_t-1, x_t, and x_t+1.
B)​u_t to be uncorrelated with x_t and x_t+1.
C) ​u_t to be correlated with x_t and x_t+1.
D) ​u_t to be correlated with x_t-1, x_t, and x_t+1.

Question 13

Which of the following tests can be used to test for heteroskedasticity in a time series?

A)Johansen test
B)Dickey-Fuller test
C) Breusch-Pagan test
D) Durbin's alternative test

Question 14

In presence of serial correlation, the OLS variance formula accurately estimates the true variance of the OLS estimator.

Question 15

Which of the following statements is true?

A)Prais-Winsten and Cochrane-Orcutt transformations are consistent when explanatory variables are not strictly exogenous.
B)The SC-robust standard errors cannot be estimated in models with lagged dependent variables.
C) The SC-robust standard errors work better after quasi-differencing a time series that is expected to be serially correlated.
D) Estimation of SC-robust standard errors is independent of the sample size.

Question 16

Which of the following statements is true?

A)When explanatory variables are not strictly exogenous, the t test for serial correlation is valid.
B)When explanatory variables are not strictly exogenous, the Durbin Watson test for serial correlation is valid.
C) Breusch-Godfrey test can be used to check for second order serial correlation.
D) White test can be used to check for second order serial correlation.

Question 17

In the presence of serial correlation:

A)estimated standard errors remain valid.
B)estimated test statistics remain valid.
C) estimated OLS values are not BLUE.
D) estimated variance does not differ from the case of no serial correlation.

Question 18

The Breusch-Godfrey test statistic follows a:

A) ²distribution.
B)t distribution.
C) normal distribution.
D) F distribution.

Question 19

In a model based on a weakly dependent time series with serial correlation and strictly exogenous explanatory variables, _____.

A)the feasible generalized least square estimates are unbiased
B)the feasible generalized least square estimates are BLUE
C) the feasible generalized least square estimates are asymptotically more efficient than OLS estimates
D) the feasible generalized least square estimates are asymptotically less efficient than OLS estimates

Question 20

Which of the following is a limitation of serial correlation-robust standard errors?

A)The serial correlation-robust standard errors are smaller than OLS standard errors when there is serial correlation.
B)The serial correlation-robust standard errors can be poorly behaved when there is substantial serial correlation and the sample size is small.
C) The serial correlation-robust standard errors cannot be calculated for autoregressive processes of an order greater than one.
D) The serial correlation-robust standard errors cannot be calculated after relaxing the assumption of homoskedasticity.

Question 21

The Cochrane-Orcutt and Prais-Winsten methods are iterative methods of feasible generalized least square (FGLS) estimation.

Question 22

FGLS estimates are efficient when explanatory variables are not strictly exogenous.

Question 23

Consistency of feasible generalized least square estimators requires the error term to be correlated with lags of the explanatory variable.

Question 24

​The serial correlation-robust standard errors are typically larger than the usual OLS standard errors when there is serial correlation.

Question 25

In time series regressions, it is advisable to check for serial correlation first, before checking for heteroskedasticity.