Sample/practice exam 2017, questions and answers PDF

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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 S United States - BUSPROG: Analytic TANDARDS: TOPICS: Stationary and Weakly Dependent Time Series KEYWORDS: Bloom’s: Knowledge 2. Covariance stationary sequences where Corr(xt + xt+h) a. unit root processes. b. trend-stationary processes.

0 as

are said to be:

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 STA United States - BUSPROG: Analytic NDARDS: TOPICS: Stationary and Weakly Dependent Time Series KEYWORDS: Bloom’s: Knowledge 2

3. A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt ) < ] 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’. Cengage Learning Testing, Powered by Cognero

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ANSWER: c RATIONALE: FEEDBACK: A stochastic process {xt: t = 1,2,….} with a finite second moment 2 [E(xt ) < ] 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 S United States - BUSPROG: Analytic TANDARDS: 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 S United States - BUSPROG: Analytic TANDARDS: 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 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

POINTS:

i.i.d. sequence with zero mean and variance process of order two. 1

Cengage Learning Testing, Powered by Cognero

2

e,

2

e

represents an moving average

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DIFFICULTY : NATIONAL S TANDARDS: TOPICS: KEYWORDS:

Easy United States - BUSPROG: Analytic Stationary and Weakly Dependent Time Series 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 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

2

e

represents a(n):

2

with zero mean and variance e, represents an autoregressive process of order one. POINTS: 1 DIFFICULTY Easy : NATIONAL S United States - BUSPROG: Analytic TANDARDS: 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 ST United States - BUSPROG: Analytic ANDARDS: 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) =

.

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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: DIFFICULTY : NATIONAL S TANDARDS: TOPICS: KEYWORDS:

1 Moderate United States - BUSPROG: Analytic Asymptotic Properties of OLS 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 S United States - BUSPROG: Analytic TANDARDS: TOPICS: Asymptotic Properties of OLS KEYWORDS: Bloom’s: Knowledge 10. Consider the model: yt = OLS is: a. E(zt1|zt2) = 0.

0

+

1zt1

+

2zt2

+ ut. Under weak dependence, the condition sufficient for consistency of

b. E(yt |zt1, zt2) = 0. c. E(ut |zt1, zt2) = 0. d. E(ut |zt1, zt2) = . ANSWER: RATIONALE:

c 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 STA United States - BUSPROG: Analytic Cengage Learning Testing, Powered by Cognero

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NDARDS: TOPICS: KEYWORDS:

Asymptotic Properties of OLS Bloom’s: Knowledge

11. The model yt = yt – 1 + et, t = 1, 2, … represents a: a. AR(2) process. b. MA(1) process. c. random walk process. d. random walk with a drift process. ANSWER: c RATIONALE: FEEDBACK: The model yt = yt – 1 + et, t = 1, 2, … represents a random walk process. POINTS: 1 DIFFICULTY: Easy NATIONAL STANDAR United States - BUSPROG: Analytic DS: TOPICS: Using Highly Persistent Time Series in Regression Analysis KEYWORDS: Bloom’s: Knowledge 12. Which of the following statements is true? a. A random walk process is stationary. b. The variance of a random walk process increases as a linear function of time. c. Adding a drift term to a random walk process makes it stationary. d. The variance of a random walk process with a drift decreases as an exponential function of time. ANSWER: b RATIONALE: FEEDBACK: The variance of a random walk process increases as a linear function of time. This is because the variance of the dependent variable is equal to t.

POINTS: DIFFICULTY : NATIONAL S TANDARDS: TOPICS: KEYWORDS:

1 Moderate United States - BUSPROG: Analytic Using Highly Persistent Time Series in Regression Analysis Bloom’s: Knowledge

13. If a process is said to be integrated of order one, or I(1), _____. a. it is stationary at level b. averages of such processes already satisfy the standard limit theorems c. the first difference of the process is weakly dependent d. it does not have a unit root ANSWER: c RATIONALE: FEEDBACK: If a process is said to be integrated of order one, or I(1), the first Cengage Learning Testing, Powered by Cognero

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POINTS: DIFFICULTY: NATIONAL STA NDARDS: TOPICS: KEYWORDS:

difference of the process is weakly dependent. 1 Moderate United States - BUSPROG: Analytic Using Highly Persistent Time Series in Regression Analysis Bloom’s: Knowledge

14. Unit root processes, such as a random walk (with or without drift), are said to be: a. integrated of order one. b. integrated of order two. c. sequentially exogenous. d. asymptotically uncorrelated. ANSWER: RATIONALE:

a FEEDBACK: Unit root processes, such as a random walk (with or without

drift), are said to be integrated of order one. POINTS: DIFFICULTY: NATIONAL STA NDARDS: TOPICS: KEYWORDS:

1 Easy United States - BUSPROG: Analytic Using Highly Persistent Time Series in Regression Analysis Bloom’s: Knowledge

15. Which of the following statements is true of dynamically complete models? a. There is scope of adding more lags to the model to better forecast the dependent variable. b. The problem of serial correlation does not exist in dynamically complete models. c. All econometric models are dynamically complete. d. Sequential endogeneity is implied by dynamic completeness.. ANSWER: b RATIONALE: FEEDBACK: The problem of serial correlation does not exist in dynamically complete models. POINTS: 1 DIFFICULTY: Moderate NATIONAL STANDA United States - BUSPROG: Analytic RDS: TOPICS: Dynamically Complete Models and the Absence of Serial Correlation KEYWORDS: Bloom’s: Knowledge 16. In the model yt = 0 + 1xt1 + 2xt2 + ….. + kxtk + ut, the explanatory variables, xt = (xt1, xt2 …., xtk), are sequentially exogenous if: a. E(ut|xt , xt-1, ……) = E(ut) = 0, t = 1,2, …. b. E(ut|xt , xt-1, ……)

E(ut) = 0, t = 1,2, ….

c. E(ut|xt , xt-1, ……) = E(ut) > 0, t = 1,2, …. d. E(ut|xt , xt-1, ……) = E(ut) = 1, t = 1,2, …. Cengage Learning Testing, Powered by Cognero

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ANSWER: RATIONALE:

a FEEDBACK: In the given model, the explanatory variables are sequentially exogenous if E(ut|xt , xt-1, ……) = E(ut) = 0, t = 1,2, ….

POINTS: DIFFICULTY: NATIONAL STA NDARDS: TOPICS: KEYWORDS:

1 Moderate United States - BUSPROG: Analytic Dynamically Complete Models and the Absence of Serial Correlation Bloom’s: knowledge

17. Which of the following is a strong assumption for static and finite distributed lag models? a. Sequential exogeneity b. Strict exogeneity c. Dynamic completeness d. Homoskedasticity ANSWER: c RATIONALE: FEEDBACK: Dynamic completeness is a strong assumption for static

and finite distributed lag models. POINTS: DIFFICULTY: NATIONAL STAN DARDS: TOPICS: KEYWORDS:

1 Easy United States - BUSPROG: Analytic Dynamically Complete Models and the Absence of Serial Correlation Bloom’s: Comprehension

18. If ut refers to the error term at time ‘ t’ and yt – 1 refers to the dependent variable at time ‘t – 1’, for an AR(1) process to be homoskedastic, it is required that: a. Var(ut|yt – 1) > Var(yt|yt-1) = 2. b. Var(ut|yt – 1) = Var(yt|yt-1) >

2

c. Var(ut|yt – 1) < Var(yt|yt-1) = d. Var(ut|yt – 1) = Var(yt|yt-1) =

2

. .

2

.

ANSWER: d RATIONALE: FEEDBACK: If ut refers to the error term at time ‘t’ and yt – 1 refers to the dependent variable at time ‘t – 1’, for an AR(1) model to be homoskedastic, it is 2 required that Var(ut|yt – 1) = Var(yt|yt-1) = . POINTS: DIFFICULTY : NATIONAL S TANDARDS: TOPICS: KEYWORDS:

1 Moderate United States - BUSPROG: Analytic The Homoskedasticity Assumption for Time Series Models Bloom’s: Knowledge

19. Covariance stationarity focuses only on the first two moments of a stochastic process. a. True Cengage Learning Testing, Powered by Cognero

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b. Fals e ANSWER: True RATIONALE: FEEDBACK: Covariance stationarity focuses only on the first two moments of a stochastic process: the mean and variance, which are constant over time. POINTS: 1 DIFFICULTY: Easy NATIONAL ST United States - BUSPROG: Analytic ANDARDS: TOPICS: Stationary and Weakly Dependent Time Series KEYWORDS: Bloom’s: Knowledge 20. Weakly dependent processes are said to be integrated of order zero. a. True b. Fals e ANSWER: True RATIONALE: FEEDBACK: Weakly dependent processes are said to be integrated of order zero, or I(0). POINTS: 1 DIFFICULTY: Easy NATIONAL STANDAR United States - BUSPROG: Analytic DS: TOPICS: Stationary and Weakly Dependent Time Series KEYWORDS: Bloom’s: Knowledge 21. If a process is a covariance stationary process, then it will have a finite second moment. a. True b. Fals e ANSWER: False RATIONALE: FEEDBACK: If a stationary process has a finite second moment, then it must be covariance stationary, but the converse is certainly not true. POINTS: 1 DIFFICULTY: Easy NATIONAL ST United States - BUSPROG: Analytic ANDARDS: TOPICS: Stationary and Weakly Dependent Time Series KEYWORDS: Bloom’s: Knowledge 22. Under adaptive expectations, the expected current value of a variable does not depend on a recently observed value of the variable. a. True b. Fals e ANSWER: False RATIONALE: FEEDBACK: Under adaptive expectations, the expected current value of a Cengage Learning Testing, Powered by Cognero

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POINTS: DIFFICULTY: NATIONAL STA NDARDS: TOPICS: KEYWORDS:

variable adapts to a recently observed value of the variable. 1 Moderate United States - BUSPROG: Analytic Asymptotic Properties of OLS Bloom’s: Knowledge

23. The variance of a random walk process decreases as a linear function of time. a. True b. Fals e ANSWER: False RATIONALE: FEEDBACK: The variance of a random walk process increases as a

linear function of time. POINTS: 1 DIFFICULTY: Easy NATIONAL STANDA United States - BUSPROG: Analytic RDS: TOPICS: Using Highly Persistent Time Series in Regression Analysis KEYWORDS: Bloom’s: Comprehension 24. Sequential exogeneity is implied by dynamic completeness. a. True b. Fals e ANSWER: True RATIONALE: FEEDBACK: Sequential exogeneity is implied by dynamic completeness. POINTS: 1 DIFFICULTY: Easy NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: KEYWORDS:

Dynamically Complete Models and the Absence of Serial Correlation Bloom’s: Knowledge

25. The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time. a. True b. Fals e ANSWER: True RATIONALE: FEEDBACK: The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time. Homeskedasticity implies that the variance of the error term is constant and hence cannot be a function of time. POINTS: 1 Cengage Learning Testing, Powered by Cognero

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DIFFICULTY : NATIONAL S TANDARDS: TOPICS: KEYWORDS:

Easy United States - BUSPROG: Analytic The Homoskedasticity Assumption for Time Series Models Bloom’s: Knowledge

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