Question 1

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

Accepted Answer

C

Question 2

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

Accepted Answer

An I(1) process means that the first difference of the process is stationary, implying weak dependence over time. This does not necessarily mean it is stationary at level (A), nor does it imply that averages of such processes satisfy standard limit theorems (B), or that it does not have a unit root (D), as having a unit root is actually a characteristic of I(1) processes before differencing.

Question 3

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < ] is covariance stationary if: A)E(x_t) is variable, Var(x_t) is variable, and for any t, h 1, Cov(x_t, x_t+h) depends only on 'h' and not on 't'. B)E(x_t) is variable, Var(x_t) is variable, and for any t, h 1, Cov(x_t, x_t+h) depends only on 't' and not on h. C)E(x_t) is constant, Var(x_t) is constant, and for any t, h 1, Cov(x_t, x_t+h) depends only on 'h' and not on 't'. D)E(x_t) is constant, Var(x_t) is constant, and for any t, h 1, Cov(x_t, x_t+h) depends only on 't' and not on 'h'.

Accepted Answer

For a covariance stationary process, the first two conditions should hold true, i.e., the mean and variance should be constant. Additionally, the covariance function should depend only on the time difference between the two points and not on their actual values. Hence, option C is the correct choice as it satisfies all the conditions. Options A and B violate the third condition, while option D violates the fourth condition.

Question 4

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.

Accepted Answer

A stationary process is one whose statistical properties, such as mean and variance, remain constant over time. When any collection of random variables in a sequence is taken and shifted ahead by h time periods, the joint probability distribution remains unchanged, indicating that the process is stationary. Option B correctly captures this property. Option A is incorrect since a stationary process should not exhibit any change in statistical properties upon shifting. Option C is incorrect since a stationary process is not expected to have serial correlation between error terms or explanatory variables, and positive covariance is not a defining property of stationarity. Option D is also incorrect since a stationary process should not exhibit serial correlation between error terms or explanatory variables, and positive covariance is not a defining property of stationarity.

Question 5

Consider the model: y_t = ₀ + ₁z_t₁ + ₂z_t₂ + u_t. Under weak dependence, the condition sufficient for consistency of OLS is: A)E(z_t₁|z_t₂) = 0. B)E(y_t |z_t₁, z_t₂) = 0. C)E(u_t |z_t₁, z_t₂) = 0. D)E(u_t |z_t₁, z_t₂) = .

Accepted Answer

Under weak dependence, the condition sufficient for consistency of OLS is that the error term u is uncorrelated with all regressors, including their lagged values. Therefore, the correct choice is C, which states that the error term u is uncorrelated with z_t₁ and z_t₂. The other choices do not capture this condition.

Question 6

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..

Accepted Answer

Dynamically complete models are designed such that the error term is not serially correlated, meaning the problem of serial correlation does not exist.

Question 7

Covariance stationarity focuses only on the first two moments of a stochastic process.

Accepted Answer

Covariance stationarity requires that the mean and covariance of a stochastic process are constant over time, which only involves the first two moments of the process.

Question 8

In the model y_t = ₀ + ₁x_t₁ + ₂x_t₂ + ….. + _kx_tk + u_t, the explanatory variables, x_t = (x_t₁, x_t₂ …., x_tk), are sequentially exogenous if: A)E(u_t|xt , xt-₁, ……) = E(u_t) = 0, t = 1,2, …. B)E(u_t|xt , xt-₁, ……) E(u_t) = 0, t = 1,2, …. C)E(u_t|xt , xt-₁, ……) = E(u_t) > 0, t = 1,2, …. D)E(u_t|xt , xt-₁, ……) = E(u_t) = 1, t = 1,2, ….

Accepted Answer

Sequential exogeneity requires that the error term u is not correlated with any of the explanatory variables or their lagged values. Therefore, the correct statement is that the error term is independent of the explanatory variables, which is captured by option A. Options B, C, and D are incorrect because they impose additional conditions that are not required for sequential exogeneity.

Question 9

The model y_t = y_{t -} ₁ + e_t, t = 1, 2, … represents a: A)AR(2) process. B)MA(1) process. C)random walk process. D)random walk with a drift process.

Accepted Answer

The given model is a random walk process because it is expressed as the current value being equal to the previous value plus a white noise error term, without any drift component.

Question 10

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.

Accepted Answer

A model with a lagged dependent variable violates the strict exogeneity assumption because the lagged dependent variable is correlated with past error terms, which are part of the information set at the time the lagged dependent variable is determined.

Question 11

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t₁, x_t₂ …., x_tk). The assumption that the errors are contemporaneously homoskedastic implies that: A)Var(u_t|x_t) = . B)Var(u_t|xt) = . C)Var(u_t|xt) = ². D)Var(u_t|x_t) = .

Accepted Answer

The answer of Suppose u_t is the error term for...

Question 12

Weakly dependent processes are said to be integrated of order zero.

Accepted Answer

This statement is true. Weakly dependent processes are those where the autocovariance function decreases to zero at a sufficiently fast rate. Such processes are said to be integrated of order zero, denoted as I(0).

Question 13

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.

Accepted Answer

A random walk process is not stationary because its mean and variance both increase with time. The variance of a random walk process increases as the square of time, not as a linear function of time. Adding a drift term to a random walk process does not make it stationary. The variance of a random walk process with a drift still increases with time, but at a slower rate than without a drift. Therefore, the correct statement is that the variance of a random walk process increases as a square function of time.

Question 14

The model x_t = ₁x_{t -} ₁+ e_t, t =1,2,…. , where e_t 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.

Accepted Answer

The answer of The model x_t = ₁x_{t -}...

Question 15

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.

Accepted Answer

Unit root processes, such as a random walk, are integrated of order one, meaning they require one level of differencing to become stationary.

Question 16

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.

Accepted Answer

The answer of Covariance stationary sequences where Corr(xt + xt+h)...

Question 17

If u_t refers to the error term at time 't' and y_{t -} ₁ refers to the dependent variable at time 't - 1', for an AR(1) process to be homoskedastic, it is required that: A)Var(u_t|y_{t -} ₁) > Var(y_t|y_t-₁) = ². B)Var(u_t|y_{t -} ₁) = Var(y_t|y_t-₁) > ². C)Var(u_t|y_{t -} ₁) < Var(y_t|y_t-₁) = ². D)Var(u_t|y_{t -} ₁) = Var(y_t|y_t-₁) = ².

Accepted Answer

For an AR(1) process to be homoskedastic, it is required that the conditional variance of the error term is constant across time. Therefore, Var(u_t|y_{t -} ₁) should be equal to Var(u_t|₁), and Var(y_t|y_t-₁) should be equal to Var(y_t|₁). Hence, the correct choice is D, which states that both variances are equal. The other choices suggest that one variance is greater than the other, which would mean the process is heteroskedastic.

Question 18

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.

Accepted Answer

Time series regression assumes that there is no perfect collinearity between the explanatory variables. This means that the independent variables are not highly correlated with each other, as this can lead to issues with estimation and interpretation of the coefficients. The other choices are not assumed in time series regression: contemporaneously endogeneity of explanatory variables is a concern, contemporaneous heteroskedasticity of error terms is a violation, and explanatory variables can have temporal ordering (as in lagged variables).

Question 19

The model y_t = e_t + ₁e_{t -} ₁ + ₂e_{t -} ₂ , t = 1, 2, ….. , where e_t 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.

Accepted Answer

The model can be rewritten as y_t = (1-phi_1*B)(1-phi_2*B)e_t. This is a moving average process of order two, where phi_1 and phi_2 are the moving average coefficients.

Question 20

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   .

Accepted Answer

The answer of A covariance stationary time series is weakly...

Quiz 11: Further Issues in Using Ols With Time Sries Data

Which of the following is a strong assumption for static and finite distributed lag models?

If a process is said to be integrated of order one, or I(1) , _____.

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < ] is covariance stationary if:

A process is stationary if:

Consider the model: y_t = ₀ + ₁z_t₁ + ₂z_t₂ + u_t. Under weak dependence, the condition sufficient for consistency of OLS is:

Which of the following statements is true of dynamically complete models?

Covariance stationarity focuses only on the first two moments of a stochastic process.

In the model y_t = ₀ + ₁x_t₁ + ₂x_t₂ + ….. + _kx_tk + u_t, the explanatory variables, x_t = (x_t₁, x_t₂ …., x_tk) , are sequentially exogenous if:

The model y_t = y_{t -} ₁ + e_t, t = 1, 2, … represents a:

Which of the following statements is true?

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t₁, x_t₂ …., x_tk) . The assumption that the errors are contemporaneously homoskedastic implies that:

Weakly dependent processes are said to be integrated of order zero.

Which of the following statements is true?

The model x_t = ₁x_{t -} ₁+ e_t, t =1,2,…. , where e_t is an i.i.d. sequence with zero mean and variance ²e represents a(n) :

Unit root processes, such as a random walk (with or without drift) , are said to be:

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

If u_t refers to the error term at time 't' and y_{t -} ₁ refers to the dependent variable at time 't - 1', for an AR(1) process to be homoskedastic, it is required that:

Which of the following is assumed in time series regression?

The model y_t = e_t + ₁e_{t -} ₁ + ₂e_{t -} ₂ , t = 1, 2, ….. , where e_t is an i.i.d. sequence with zero mean and variance ²e represents a(n) :

A covariance stationary time series is weakly dependent if:

Quiz 11: Further Issues in Using Ols With Time Sries Data

Which of the following is a strong assumption for static and finite distributed lag models?​

If a process is said to be integrated of order one, or I(1) , _____.

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

A process is stationary if:

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

Which of the following statements is true of dynamically complete models?

Covariance stationarity focuses only on the first two moments of a stochastic process.

In the model yt = 0 + 1xt1 + 2xt2 + ….. + kxtk + ut, the explanatory variables, xt = (xt1, xt2 …., xtk) , are sequentially exogenous if:

The model yt = yt - 1 + et, t = 1, 2, … represents a:

Which of the following statements is true?

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:

Weakly dependent processes are said to be integrated of order zero.

Which of the following statements is true?

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) :

Unit root processes, such as a random walk (with or without drift) , are said to be:​

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

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:

Which of the following is assumed in time series regression?

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 covariance stationary time series is weakly dependent if:

Which of the following is a strong assumption for static and finite distributed lag models?

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < ] is covariance stationary if:

Consider the model: y_t = ₀ + ₁z_t₁ + ₂z_t₂ + u_t. Under weak dependence, the condition sufficient for consistency of OLS is:

In the model y_t = ₀ + ₁x_t₁ + ₂x_t₂ + ….. + _kx_tk + u_t, the explanatory variables, x_t = (x_t₁, x_t₂ …., x_tk) , are sequentially exogenous if:

The model y_t = y_{t -} ₁ + e_t, t = 1, 2, … represents a:

Suppose u_t is the error term for time period 't' in a time series regression model the explanatory variables are x_t = (x_t₁, x_t₂ …., x_tk) . The assumption that the errors are contemporaneously homoskedastic implies that:

The model x_t = ₁x_{t -} ₁+ e_t, t =1,2,…. , where e_t is an i.i.d. sequence with zero mean and variance ²e represents a(n) :

Unit root processes, such as a random walk (with or without drift) , are said to be:

If u_t refers to the error term at time 't' and y_{t -} ₁ refers to the dependent variable at time 't - 1', for an AR(1) process to be homoskedastic, it is required that:

The model y_t = e_t + ₁e_{t -} ₁ + ₂e_{t -} ₂ , t = 1, 2, ….. , where e_t is an i.i.d. sequence with zero mean and variance ²e represents a(n) :