Chapter 11
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.
2. A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt2) < ∞] 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’.
3. 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 → ∞.
4. The model yt = et + β1et – 1 + β2et – 2 , t = 1, 2, ….. , where et is an i.i.d. sequence with zero mean and
variance σ2e 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.
5. The model xt = α1xt – 1 + et , t =1,2,…. , where et is an i.i.d. sequence with zero mean and variance σ2e
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.
6. 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.
7. 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) = √σ.
b. Var(ut|xt) = ∞.
c. Var(ut|xt) = σ2.
d. Var(ut|xt) = σ.
8. 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.
9. Consider the model: yt = α0 + α1rt1 + α2rt2 + ut. Under weak dependence, the condition sufficient for
consistency of OLS is:
a. E(rt1|rt2) = 0.
b. E(yt |rt1, rt2) = 0.
c. E(ut |rt1, rt2) = 0.
d. E(ut |rt1, rt2) = ∞.
10. 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.
11. 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.
12. 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
13. 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..
14. In the model yt = α0 + α1xt1 + α2xt2 + ….. + αkxtk + 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, ….
15. 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) = σ2.
b. Var(ut|yt – 1) = Var(yt|yt-1) > σ2.
c. Var(ut|yt – 1) < Var(yt|yt-1) = σ2.
d. Var(ut|yt – 1) = Var(yt|yt-1) = σ2.
16. Covariance stationarity focusses only on the first two moments of a stochastic process.
17. Under adaptive expectations, the expected current value of a variable does not depend on a recently
observed value of the variable.
18. Weakly dependent processes are said to be integrated of order zero.
19. Sequential exogeneity is implied by dynamic completeness.
20. The homoskedasticity assumption in time series regression suggests that the variance of the error
term cannot be a function of time.