Question 1

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

Covariance stationary sequences where Corr(xt + xt+h) 11eab06d_2552_847a_beed_4518ea2afedc_TB2133_11 0 as 11eab06d_2552_847b_beed_3fdc79f8b62e_TB2133_11 are said to be asymptotically uncorrelated.

Question 2

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 variables used in the regression model should not be highly correlated with each other. Option B is incorrect because time series regression assumes that the explanatory variables are exogenous, not endogenous. Option C is incorrect because time series regression assumes that the error terms are homoskedastic, not heteroskedastic. Option D is incorrect because the explanatory variables in time series regression must have temporal ordering, meaning that they are measured at regular intervals over time. One of the assumptions of time series regression is that there should be no perfect collinearity between the explanatory variables.

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 stochastic process to be covariance stationary, it needs to have constant mean and variance, which is satisfied in option C. Additionally, the covariance between x at time t and x at time t+h should only depend on h (and not on t), which is also satisfied in option C. The other options do not satisfy either one or both of these conditions for covariance stationarity. A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²) < 11eab06d_2553_20c1_beed_4521bfba7b57_TB2133_11 ] is covariance stationary if E(x_t) is constant, Var(x_t) is constant, and for any t, h 11eab06d_2553_47d2_beed_9d524913df6b_TB2133_11 1, Cov(x_t, x_t+h) depends only on 'h' and not on 't'.

Question 4

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 cannot satisfy the strict exogeneity assumption. When explanatory variables are correlated with the past, strict exogeneity does not hold.

Question 5

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

If u_t is the error term for time period 't' and x_t is a matrix consisting of all independent variables for time 't', the assumption of contemporaneously homoskedasticity implies that Var(u_t|x_t) = 11eab06d_2556_2e1c_beed_bfd583c53dd4_TB2133_11 ².

Question 6

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 (with or without drift), are integrated of order one, which means they exhibit a tendency to revert to a constant level over time, but the deviations from this level accumulate and do not disappear. Unit root processes, such as a random walk (with or without drift), are said to be integrated of order one. u200b

Question 7

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 given model is a moving average process of order two, as it has two lagged terms of the error term, eS1U1B1tS1U1B0, and no lagged terms of the dependent variable, S1U1B0. The model y_t = e_t + 11eab06d_2554_a771_beed_c57aba2e5eb9_TB2133_11 ₁e_{t -} ₁ + 11eab06d_2554_ce82_beed_41ed038b063b_TB2133_11 ₂e_{t -} ₂ , t = 1, 2, ….. , where e_t is an i.i.d. sequence with zero mean and variance 11eab06d_2554_ce83_beed_913b9f92a6f8_TB2133_00 ²e, represents an moving average process of order two.

Question 8

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

If a process is said to be integrated of order one, or I(1), the first difference of the process is weakly dependent.

Question 9

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 those that have included all relevant lags of the dependent variable and explanatory variables. Therefore, there is no scope of adding more lags to the model. However, the problem of serial correlation may still exist in dynamically complete models. Not all econometric models are dynamically complete, and sequential endogeneity is not necessarily implied by dynamic completeness. The problem of serial correlation does not exist in dynamically complete models.

Question 10

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

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 11eab06d_2554_0b2c_beed_8d5aa4fbf861_TB2133_11 11eab06d_2554_323d_beed_f7430fa080fd_TB2133_11 .

Question 11

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 where the statistical properties (mean, variance, covariance) of the process do not change over time. Option B correctly captures this by stating that if any collection of random variables in a sequence is shifted ahead by h time periods, the joint probability distribution remains unchanged (i.e. the statistical properties of the process remain constant over time). Options A, C, and D are not accurate definitions of a stationary process. 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.

Question 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.

Accepted Answer

The variance of a random walk process increases as a function of time because as time passes, the random walk process accumulates more and more random shocks, leading to increasingly larger fluctuations. 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 11eab06d_2557_1881_beed_97bfb9b4decb_TB2133_11 t.

Question 13

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 must be uncorrelated with the regressors conditional on the lagged dependent variables. Therefore, the correct choice is C, which states that the error term should be uncorrelated with the regressors conditional on lagged dependent variables. The other choices do not correctly state the condition for consistency of OLS. If a time series model is weakly dependent, the condition sufficient for consistency of OLS is E(u_t|z_t₁, z_t₂) = 0.

Question 14

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, the variance of the error term at time 't' (u_t) conditioned on the dependent variable at time 't - 1' (y_{t -} ₁) should be equal to the variance of the dependent variable at time 't' (y_t) conditioned on the same lagged variable (y_{t -} ₁). Therefore, the correct option is (D). None of the other options present this condition. 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) model to be homoskedastic, it is required that Var(u_t|y_{t -} ₁) = Var(y_t|y_t-1) = 11eab06d_2558_9f2b_beed_67cb9774980a_TB2133_11 ².

Question 15

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

Accepted Answer

Weakly dependent processes have a memoryless property, which means the current value of the process does not depend on its past values. This property is inherent in processes integrated of order zero, which have no persistence in their dynamics. Weakly dependent processes are said to be integrated of order zero, or I(0).

Question 16

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 is not correlated with any of the previous or current values of the explanatory variables, which is captured by the condition E(u|xt, xt-₁,…) = E(u) = 0. This means that the error term is not affected by the values of the explanatory variables, hence they are exogenous. Choice B is incorrect because it implies that the error term is perfectly predictable based on the values of the explanatory variables, which violates the assumption of exogeneity. Choices C and D are also incorrect because they imply a positive or non-zero correlation between the error term and the explanatory variables, respectively, which also violates the assumption of exogeneity. In the given model, the explanatory variables are sequentially exogenous if E(u_t|xt , xt-1, ……) = E(u_t) = 0, t = 1,2, ….

Question 17

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 model x_t = 11eab06d_2555_43b6_beed_cd86112acc23_TB2133_11 ₁x_{t -}₁+ e_t, t =1,2,…. , where e_t is an i.i.d. sequence with zero mean and variance 11eab06d_2555_6ac7_beed_9b6118e65d09_TB2133_11 ²_e, represents an autoregressive process of order one.

Question 18

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 model y_t = y_{t -} ₁ + e_t, t = 1, 2, … represents a random walk process.

Question 19

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

Accepted Answer

Covariance stationarity only requires that the mean and covariance (first two moments) of a stochastic process are constant over time, and does not consider higher moments. Covariance stationarity focuses only on the first two moments of a stochastic process: the mean and variance, which are constant over time.

Question 20

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

Dynamic completeness is a strong assumption for static and finite distributed lag models. u200b

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

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

Which of the following is assumed in time series regression?

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

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:

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

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) :

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

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

A covariance stationary time series is weakly dependent if:

A process is stationary if:

Which of the following statements is true?

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

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:

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

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 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) :

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

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

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

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

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

Which of the following is assumed in time series regression?

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

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:

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

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) :

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

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

A covariance stationary time series is weakly dependent if:

A process is stationary if:

Which of the following statements is true?

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

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:

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

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

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) :

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

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

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:

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:

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

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) :

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

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:

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 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) :

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

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