1. A process is stationary if:

a. any collection of random variables in a sequence is taken and shifted ahead by h time periods; the joint probability distribution changes.

b. any collection of random variables in a sequence is taken and shifted ahead by h time periods, the joint probability distribution remains unchanged.

c. there is serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.

d. there is no serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.

ANSWER: b

RATIONALE: FEEDBACK: A process is stationary if any collection of random variables in a sequence is taken and shifted ahead by h time periods; the joint probability distribution remains unchanged.

POINTS: 1

DIFFICULTY: Moderate

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

2. Covariance stationary sequences where Corr(xt + xt+h) 0 as are said to be:

a. unit root processes.

b. trend-stationary processes.

c. serially uncorrelated.

d. asymptotically uncorrelated.

ANSWER: d

RATIONALE: FEEDBACK: Covariance stationary sequences where Corr(xt + xt+h) 0 as are said to be asymptotically uncorrelated.

POINTS: 1

DIFFICULTY: Easy

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

3. A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt2) < ] is covariance stationary if:

a. E(xt) is variable, Var(xt) is variable, and for any t, h 1, Cov(xt, xt+h) depends only on ‘h’ and not on ‘t’.

b. E(xt) is variable, Var(xt) is variable, and for any t, h 1, Cov(xt, xt+h) depends only on ‘t’ and not on h.

c. E(xt) is constant, Var(xt) is constant, and for any t, h 1, Cov(xt, xt+h) depends only on ‘h’ and not on ‘t’.

d. E(xt) is constant, Var(xt) is constant, and for any t, h 1, Cov(xt, xt+h) depends only on ‘t’ and not on ‘h’.

ANSWER: c

RATIONALE: FEEDBACK: A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt2) < ] is covariance stationary if E(xt) is constant, Var(xt) is constant, and for any t, h 1, Cov(xt, xt+h) depends only on ‘h’ and not on ‘t’.

POINTS: 1

DIFFICULTY: Moderate

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

4. A covariance stationary time series is weakly dependent if:

a. the correlation between the independent variable at time ‘t’ and the dependent variable at time ‘t + h’ goes to as h 0.

b. the correlation between the independent variable at time ‘t’ and the dependent variable at time ‘t + h’ goes to 0 as h .

c. the correlation between the independent variable at time ‘t’ and the independent variable at time ‘t + h’ goes to 0 as h .

d. the correlation between the independent variable at time ‘t’ and the independent variable at time ‘t + h’ goes to as h .

ANSWER: c

RATIONALE: FEEDBACK: A covariance stationary time series is weakly dependent if the correlation between the independent variable at time ‘t’ and the independent variable at time ‘t + h’ goes to 0 as h .

POINTS: 1

DIFFICULTY: Easy

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

5. The model yt = et + 1et – 1 + 2et – 2 , t = 1, 2, ….. , where et is an i.i.d. sequence with zero mean and variance 2e represents a(n):

a. static model.

b. moving average process of order one.

c. moving average process of order two.

d. autoregressive process of order two.

ANSWER: c

RATIONALE: FEEDBACK: The model yt = et + 1et – 1 + 2et – 2 , t = 1, 2, ….. , where et is an i.i.d. sequence with zero mean and variance 2e, represents an moving average process of order two.

POINTS: 1

DIFFICULTY: Easy

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

6. The model xt = 1xt – 1 + et, t =1,2,…. , where et is an i.i.d. sequence with zero mean and variance 2e represents a(n):

a. moving average process of order one.

b. moving average process of order two.

c. autoregressive process of order one.

d. autoregressive process of order two.

ANSWER: c

RATIONALE: FEEDBACK: The model xt = 1xt – 1 + et, t =1,2,…. , where et is an i.i.d. sequence with zero mean and variance 2e, represents an autoregressive process of order one.

POINTS: 1

DIFFICULTY: Easy

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Stationary and Weakly Dependent Time Series

KEYWORDS: Bloom’s: Knowledge

7. Which of the following is assumed in time series regression?

a. There is no perfect collinearity between the explanatory variables.

b. The explanatory variables are contemporaneously endogenous.

c. The error terms are contemporaneously heteroskedastic.

d. The explanatory variables cannot have temporal ordering.

ANSWER: a

RATIONALE: FEEDBACK: One of the assumptions of time series regression is that there should be no perfect collinearity between the explanatory variables.

POINTS: 1

DIFFICULTY: Easy

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Asymptotic Properties of OLS

KEYWORDS: Bloom’s: Knowledge

8. Suppose ut is the error term for time period ‘t’ in a time series regression model the explanatory variables are xt = (xt1, xt2 …., xtk). The assumption that the errors are contemporaneously homoskedastic implies that:

a. Var(ut|xt) = .

b. Var(ut|xt) = .

c. Var(ut|xt) = 2.

d. Var(ut|xt) = .

ANSWER: c

RATIONALE: FEEDBACK: If ut is the error term for time period ‘t’ and xt is a matrix consisting of all independent variables for time ‘t’, the assumption of contemporaneously homoskedasticity implies that Var(ut|xt) = 2.

POINTS: 1

DIFFICULTY: Moderate

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Asymptotic Properties of OLS

KEYWORDS: Bloom’s: Knowledge

9. Which of the following statements is true?

a. A model with a lagged dependent variable cannot satisfy the strict exogeneity assumption.

b. Stationarity is critical for OLS to have its standard asymptotic properties.

c. Efficient static models can be estimated for nonstationary time series.

d. In an autoregressive model, the dependent variable in the current time period varies with the error term of previous time periods.

ANSWER: a

RATIONALE: FEEDBACK: A model with a lagged dependent variable cannot satisfy the strict exogeneity assumption. When explanatory variables are correlated with the past, strict exogeneity does not hold.

POINTS: 1

DIFFICULTY: Moderate

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Asymptotic Properties of OLS

KEYWORDS: Bloom’s: Knowledge

10. Consider the model: yt = 0 + 1zt1 + 2zt2 + ut. Under weak dependence, the condition sufficient for consistency of OLS is:

a. E(zt1|zt2) = 0.

b. E(yt |zt1, zt2) = 0.

c. E(ut |zt1, zt2) = 0.

d. E(ut |zt1, zt2) = .

ANSWER: c

RATIONALE: FEEDBACK: If a time series model is weakly dependent, the condition sufficient for consistency of OLS is E(ut|zt1, zt2) = 0.

POINTS: 1

DIFFICULTY: Moderate

NATIONAL STANDARDS: United States – BUSPROG: Analytic

TOPICS: Asymptotic Properties of OLS

KEYWORDS: Bloom’s: Knowledge

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