Deck 11: Auto-Correlation

Question 1

The autoregressive structure of the error term is the current-period error term and

A)the dependent variable.
B)the independent variables.
C)prior-period error terms.
D)future-period error terms.

Answer 1

C

Question 2

The second stage of the Durbin-Watson test for the presence of autocorrelation is to

A)regress the current period residuals on the residuals lagged one period.
B)regress the residuals lagged one period on the current period residuals.
C)calculate the test statistic
D)calculate the test statistic

Answer 2

D

Question 3

Because it violates time-series assumption ____,autocorrelation results in estimates that are ____.

A)T6;biased
B)T6;inefficient
C)T6;unbiased
D)T4;inefficient

Answer 3

B

Question 4

Autoregressive error terms are potentially problematic because they result in

A)biased parameter estimates.
B)estimated standard errors that are incorrect.
C)estimated standard errors that are always too small.
D)incorrect estimated slope coefficients.

Question 5

Suppose that you plot the residuals from a regression of Number of Wins on Payroll for the Dallas Cowboys over the last 20 years and you get the following
You would conclude that

A)definitely autocorrelated.
B)likely not autocorrelated.
C)possibly autocorrelated and you would perform a formal test for heteroskedasticity.
D)possibly autocorrelated and you would always perform a correction for autocorrelation.

Question 6

A simple method for determining whether autocorrelation is present in a given data set is to

A)construct a histogram.
B)calculate the variance of the sample.
C)examine the residual plot.
D)plot the data points from smallest to largest.

Question 7

Autocorrelation occurs when

A)an omitted independent variable is correlated with the error term.
B)the error term is correlated across different time-periods.
C)the error term has a non-constant variance.
D)the error term is,on average,equal to zero.

Question 8

The most likely violation of the assumptions required for OLS to be BLUE when dealing with time-series data is referred to as

A)heteroskedasticity.
B)homeskedasticity.
C)autocorrelation.
D)autoskedasticity.

Question 9

Autocorrelation is a problem because it causes the

A)estimated slope coefficients to be biased.
B)estimated standard errors to be incorrect.
C)data to be spuriously correlated.
D)estimated standard errors to always be too small.

Question 10

Autocorrelation violates the time-series assumption

A)T3.
B)T4.
C)T5.
D)T6.

Question 11

The null hypothesis for testing for the presence of autocorrelation is

A)the error terms are correlated over time.
B)the error terms are not correlated over time.
C)the error terms follow an AR(1)process.
D)the error terms have constant variance over time.

Question 12

An AR(2)process is written as

A)
B)
C)
D)

Question 13

The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the model and determine

A)the current period residuals.
B)the residuals lagged one period.
C)the current period residuals and the residuals lagged one period.
D)the current period residuals,the residuals lagged one period,and the residuals lagged two periods.

Question 14

An AR(1,6)process is written as

A)
B)
C)
D)

Question 15

An AR(1)process is written as

A)
B)
C)
D)

Question 16

If autocorrelation is not present,then the Durbin-Watson test statistic will be

A)near 0.
B)near 2.
C)near 4.
D)between 0 and 1.

Question 17

Suppose that you plot the residuals from a regression of GDP on the unemployment rate and you get the following
You would conclude that the error terms are

A)definitely autocorrelated.
B)likely not autocorrelated.
C)possibly autocorrelated and you would perform a formal test for autocorrelation.
D)possibly autocorrelated and you would perform a correction for heteroskedasticity.

Question 18

If positive autocorrelation is not present,then the Durbin-Watson test statistic will be

A)closer to 0.
B)closer to 2.
C)closer to 4.
D)greater than 3.

Question 19

The third step of the Regression test for AR(1)is to estimate the model

A)
B)
C)
D)

Question 20

The first step of the Regression test for the presence of AR(1)is to estimate the model and determine

A)the current period squared residuals.
B)the residuals lagged one period.
C)the current period residuals and the residuals lagged one period.
D)the current period residuals,the residuals lagged one period,and the residuals lagged two periods.

Question 21

The final step of the Regression test for AR(1)is to perform

A)an F-test for the joint significance of ρ₁ and ρ₂.
B)an F-test for the overall significance of the x_t and e_{t - 1}.
C)a t-test for the individual significance of ρ.
D)separate t-tests for the individual significance of ρ₁ and ρ₂.

Question 22

In order to perform cointegration,you need to identify

A)a second independent variable that is correlated with the dependent variable but uncorrelated with the first independent variable.
B)an independent variable that moves with the dependent variable and produces residuals that are I(0)when the dependent variable is regressed on it.
C)an independent variable that moves with the dependent variable and produces residuals that are I(1)when the dependent variable is regressed on it.
D)an independent variable that moves with the dependent variable and produces non-stationary residuals.

Question 23

What are the null and alternative hypotheses for testing for the presence of AR(1)autocorrelation? Why? Explain.

Question 24

Write out the model for an AR(1)process.Explain what it means.Repeat for an AR(2)process.

Question 25

You can determine whether a unit root exists by performing

A)a Newey-West test.
B)a Cochrane-Orcutt test.
C)a Prais-Winsten test.
D)a Dickey-Fuller test.

Question 26

The Cochrane-Orcutt method is

A)an iterative process for determining whether autocorrelation exists.
B)an iterative process for correcting for the presence of autocorrelation.
C)a one-step process for determining whether autocorrelation exists.
D)a one-step process for correcting for the presence of heteroskedasticity.

Question 27

How do you perform the Durbin-Watson test for autocorrelation? Explain.

Question 28

If a unit root exists,then

A)there is no issue with estimating time-series models.
B)steps must be taken to make the time-series a stable AR(1).
C)it is impossible to model the AR(1)process.
D)the time-series is not an AR(1)process.

Question 29

Iterations in the Cochrane-Orcutt method for AR(1)should be continued until

A)
B)
C) changes by .05 between iterations.
D) is stable between iterations.

Question 30

Suppose that you are performing the Regression test for AR(1)and you get (standard errors in parentheses)with 50 observations
You would conclude that

A)autocorrelation is not present in the data.
B)autocorrelation is present in the data.
C)heteroskedasticity is not present in the data.
D)heteroskedasticity is present in the data.

Question 31

The third step in the first iteration of the Cochrane-Orcutt method for AR(1)is to

A)use the estimate of to adjust the dependent variable.
B)use the estimate of to adjust the independent variables.
C)use the estimate of to adjust the dependent variable and the independent variables.
D)use the estimate of and to adjust the dependent variable and the independent variables.

Question 32

Newey-West robust standard errors

A)the preferred method for correcting for potential autocorrelation.
B)calculated through an iterative process.
C)automatically calculated in Excel.
D)the result of performing the Prais-Winsten method.

Question 33

The first step in the first iteration of the Cochrane-Orcutt method for AR(1)is to estimate the model and determine

A)the current period residuals.
B)the residuals lagged one period.
C)the current period residuals and the residuals lagged one period.
D)the current period residuals,the residuals lagged one period,and the residuals lagged two periods.

Question 34

What is autocorrelation? Why is it problematic? Explain.

Question 35

Conintegration is

A)an iterative process for removing a unit root.
B)an iterative process for correcting the data for the presence of autocorrelation.
C)an empirical method for removing a unit root.
D)an empirical method for making a time-series I(1).

Question 36

A potential shortcoming of the Cochrane-Orcutt method for AR(1)is that it

A)drops the first the first two observations.
B)drops the first observation.
C)does not typcially estimate correctly.
D) no longer changes between iterations.

Question 37

The second step in the first iteration of the Cochrane-Orcutt method for AR(1)is to estimate the model

A) to generate an estimate of .
B) to generate an estimate of .
C) to generate an estimate of and .
D) to generate an estimate of .

Question 38

The second iteration of the Cochrane-Orcutt method for AR(1)involves

A)repeating the process in the first iteration for the data adjusted by and .
B)repeating the process in the first iteration for the data adjusted by .
C)re-estimating following the process in the first iteration.
D)re-estimating using the data lagged one period.

Question 39

A unit root exists when

A)the parameter on the AR(1)process is equal to 0.
B)an explosive time-series exists.
C)a time-series is a stable AR(1).
D)the parameter on the AR(1)process is equal to 1.

Question 40

The Prais-Winsten procedure for AR(1)improves on the Cochrane-Orcutt method for AR(1)by

A)incorporating estimates of the first observation only in the first iteration.
B)incorporating estimates of the first observation in all iterations.
C)generating an estimate of that actually equals ρ.
D)reducing the required number of iterations.

Question 41

What is the potential shortcoming of the Cochrane-Orcutt method for AR(1)processes? Why is it a concern? How do you correct for it? Explain.

Question 42

How do you perform the Cochrane-Orcutt method for AR(1)processes? Explain.

Question 43

Suppose you are interested in explaining variation in quarterly Net Exports (billions)and that you estimate the regression function (standard errors in parentheses)
a)How many years' worth of data do you have? How can you tell? Explain.
b)Do you suspect that autocorrelation might be present in this model? If so,what type? Why? Explain.
c)How would you use the Regression test for AR(1)to determine whether autocorrelation is present? Explain.
d)Suppose you know that the autocorrelation follows an AR(1)process.How would you use the Prais-Winsten method to correct for the autocorrelation? Explain.
e)When using the Prais-Winsten method,how many observations will you have in your final analysis? Why? Explain.

Question 44

How do you perform Prais-Winsten method for AR(1)processes? Explain.

Question 45

What is a unit root? Why is it problematic? Explain.

Question 46

Suppose you are interested in explaining variation in monthly Ice Cream consumption (thousands of gallons)and that you estimate the regression function (standard errors in parentheses)
a)How many years' worth of data do you have? How can you tell? Explain.
b)Do you suspect that autocorrelation might be present in this model? If so,what type? Why? Explain.
c)How would you use the Durbin-Watson test to determine whether autocorrelation is present? Explain.What type of autoregressive process does the Durbin-Watson test work for?
d)Suppose you know that the autocorrelation follows an AR(1)process.How would you use the Cochrane-Orcutt method to correct for the autocorrelation? Explain.
e)When using the Cochrane-Orcutt method,how many observations will you have in your final analysis? Why? Explain.

Question 47

Why are Newey-West robust standard errors the preferred method for dealing with potential autocorrelation? Explain.

Question 48

What is the intuition behind the Regression test for AR(1)? Explain.

Question 49

How do you perform the Regression test for AR(1)? Explain.

Question 50

Suppose you are interested in explaining variation in annual Defense Spending (billions)and that you estimate the regression function (standard errors in parentheses)
a)How many years' worth of data do you have? How can you tell? Explain.
b)Do you suspect that autocorrelation might be present in this model? If so,what type? Why? Explain.
c)How would you use the Regression test for AR(2)to determine whether autocorrelation is present? Explain.
d)What is the preferred method of correct for potential autocorrelation? Why is it preferred? Explain.
Suppose you are interested in explaining variation in annual Defense Spending (billions)and that you estimate the sample regression function (standard errors in parentheses)