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

Question 1

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

Answer 1

False

Question 2

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 2

B

Question 3

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 3

A

Question 4

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)= √σ.
B)Var(u_t|x_t)= ∞.
C)Var(u_t|x_t)= σ².
D)Var(u_t|x_t)= σ.

Question 5

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 6

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

Question 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.

Question 8

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 9

Sequential exogeneity is implied by dynamic completeness.

Question 10

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

Question 11

Consider the model: y_t = α₀ + α₁r_t1 + α₂r_t2 + u_t.Under weak dependence,the condition sufficient for consistency of OLS is:

A)E(r_t1|r_t2)= 0.
B)E(y_t |r_t1,r_t2)= 0.
C)E(u_t |r_t1,r_t2)= 0.
D)E(u_t |r_t1,r_t2)= ∞.

Question 12

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'.

Question 13

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

Question 14

In the model y_t = α₀ + α₁x_t1 + α₂x_t2 + …..+ α?_kx_tk + u_t,the explanatory variables,x_t = (x_t1,x_t2 …. ,x_tk),are sequentially exogenous if:

A)E(u_t|x_t,x_t-1,……)= E(u_t)= 0,t = 1,2,….
B)E(u_t|x_t,x_t-1,……)≠ E(u_t)= 0,t = 1,2,….
C)E(u_t|x_t,x_t-1,……)= E(u_t)> 0,t = 1,2,….
D)E(u_t|x_t,x_t-1,……)= E(u_t)= 1,t = 1,2,….

Question 15

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)= σ².
B)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)> σ².
C)Var(u_t|y_{t - 1})< Var(y_t|y_t-1)= σ².
D)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)= σ².

Question 16

The model x_t? = α₁x_{t - 1} + e_t ,t =1,2,…. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_e 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 17

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 18

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 ∞ as h → 0.
D)the correlation between the independent variable at time 't' and the independent variable at time 't + h' goes to 0 as h → ∞.

Question 19

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

Question 20

The model y_t = e_t + β₁e_{t - 1} + β₂e_{t - 2} ,t = 1,2,….. ,where e_t is an i.i.d.sequence with zero mean and variance σ²_erepresents 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.