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

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

Answer 1

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

Answer 2

C

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'.

Answer 3

C

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.

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) = .

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..

Question 7

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

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.

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.

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) = .

Question 12

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

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.

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.

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.

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.

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.

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.

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.

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 .

Question 21

The homoskedasticity assumption in time series regression suggests that the variance of the error term cannot be a function of time.

Question 22

If a process is a covariance stationary process, then it will have a finite second moment.

Question 23

Which of the following is true if y_t = + + + + u_t is a dynamically complete model?

A)E(y_t| x_t , y_{t -1}, x_{t -1}) = E(y_t| x_t , y_{t -1}, x_{t -1,}……)
B)E(y_t| x_t , y_{t -1}, x_{t -1}) = 0
C)E(y_t| x_t , y_{t -1}, x_{t -1}) = E(y_{t -1}) + E(x_t) + E(x_{t -1})
D)E(y_t| x_t , y_{t -1}, x_{t -1}) = E(y_t)

Question 24

Under adaptive expectations, the expected current value of a variable does not depend on a recently observed value of the variable.

Question 25

The first difference of an I(1) time series is weakly dependent.

Question 26

The variance of a random walk process decreases as a linear function of time.​

Question 27

If adding one more lag of the dependent variable would explain the dependent variable better, then the model is not dynamically complete.

Question 28

Sequential exogeneity is implied by dynamic completeness.