Chapter 18
1. Let {(yt, zt): t = …, 2, 1, 0, 1, 2, …} be a bivariate time series process. The model: yt = α + βozt + β1zt –
1 + β2zt – 2 + ….. + ut, where t = …..,–2,–1,0,1,2,……, represents a(n):
a. moving average model.
b. ARIMA model.
c. finite distributed lag model.
d. infinite distributed lag model.
2. The Koyck distributed lag model is an example of:
a. a moving average model.
b. an autoregressive conditional heteroskedasticity model.
c. an infinite distributed lag model.
d. a finite distributed lag model.
3. The model: yt = α0 + γ0zt +ρyt – 1 + γ1zt – 1 +vt, where vt = ut – ρut – 1 represents a:
a. finite distributed lag model.
b. simultaneous equations model.
c. rational distributed lag model.
d. vector error correction model.
4. In the given AR(1) model, yt = α + ρyt – 1, t = 1,2…… , the Dickey-Fuller distribution refers to the:
a. asymptotic distribution of the t statistic under the hypothesis ρ – 1 = 0.
b. asymptotic distribution of the F statistic under the hypothesis ρ – 1 = 0.
c. asymptotic distribution of the χ2 statistic under the hypothesis ρ – 1 = 0.
d. asymptotic distribution of the z statistic under the hypothesis ρ – 1 = 0.
5. Which of the following is used to test whether a time series follows a unit root process?
a. Wald test
b. White test
c. Augmented Dickey-Fuller test
d. Johansen test
6. A spurious correlation refers to a situation where:
a. two variables are related through their correlation with a third variable.
b. the correlation coefficient between two variables cannot be estimated.
c. there is direct causal relationship between two variables but tests for correlations reject this
relationship.
d. the correlation between two variables is positive till the sample size reaches a threshold, and negative
after the sample size crosses the threshold.
7. A spurious regression refers to a situation where:
a. the direction of the relationship between the dependent variable and the explanatory variables is
uncertain.
b. even though two variables are independent, the OLS regression of one variable on the other indicates
a relationship between them.
c. a few important and necessary explanatory variables are left out of a regression equation, thus
leading to inefficient and inconsistent forecasts.
d. at least one of the variables used in a regression equation does not have a unit root and the error
terms are heteroskedastic.
8. Which of the following statements is true of spurious regressions?
a. The OLS estimates of the population parameters are efficient and unbiased and the t statistic is valid.
b. Even if the explanatory variables and the dependent variable are independent times series processes,
the R2 can large.
c. Spurious regressions are limited to I(0) processes, and are not possible in case of I(1) processes.
d. Spurious regressions are limited to I(1) processes, and are not possible in case of I(0) processes.
9. Two series are said to be cointegrated if:
a. both series are I(1) but a linear combination of them is I(0).
b. both series are I(0) but a linear combination of them is I(1).
c. both series have the same set of explanatory variables but a different dependent variable.
d. both series have the same dependent variable but a different set of explanatory variables.
10. Which of the following tests can be used to check for cointegration between two series?
a. Wald test
b. Breush-Pagan test
c. White test
d. Engle-Granger test
11. Which of the following statements is true?
a. The calculated t statistic is valid and efficient in case of a spurious regression.
b. If an explanatory variable or a dependent variable is integrated of the order one, the OLS estimators
are asymptotically normally distributed.
c. An error correction model can be used to study the short-run dynamics in the relationship between
the dependent variable and the explanatory variables in a time series model.
d. The Dickey-Fuller test can be used to test for heteroskedasticity in the error terms.
12. If ft denotes the forecast of yt+1 made at time t, then the forecast error is given by:
a. et+1 = ft/yt+1.
b. et+1 = yt+1/ft.
c. et+1 = yt+1 + ft.
d. et+1 = yt+1 – ft.
13. Which of the following is true of squared forecast errors?
a. An error of +4 yields a greater loss than an error of -4.
b. An error of -4 yields a greater loss than an error of +4.
c. An error of –4 or +4 yields the same loss.
d. Loss from positive and negative forecast errors cannot be compared.
14. Which of the following statements correctly identifies the difference between an autoregressive
model and a vector autoregressive model?
a. In an autoregressive model, the dependent variable is expressed as a function of its own lag, whereas
in a vector autoregressive model, the dependent variable is expressed as a function of the lag of an
explanatory variable.
b. In an autoregressive model, the dependent variable is expressed as a function of the lag of an
explanatory variable, whereas in a vector autoregressive model, the dependent variable is expressed as
a function of its own lag.
c. In an autoregressive model several series are modelled in terms of their own past, whereas in a vector
autoregressive model only one series is modelled in terms of its own past.
d. In an autoregressive model one series is modelled in terms of its own past, whereas in a vector
autoregressive model several series are modelled in terms of their past.
15. In case of forecasts, the root mean squared error is the:
a. average of the forecast errors divided by the variance of the errors.
b. average of the absolute forecast errors.
c. standard deviation of the forecast errors without any degrees of freedom adjustment.
d. standard deviation of the forecast errors with a degrees of freedom adjustment.
16. If the t statistic for the presence of a unit root in a variable is -7.22 and the 5% critical value is -2.86,
there is strong evidence against a unit root in the variable.
17. The R2 calculated in a spurious regression is a valid and efficient estimate of the goodness-of-fit of
the regression equation.
18. Exponential smoothing is a forecasting method where the weights on the lagged dependent variable
decline to zero exponentially.
19. In calculation of squared forecast errors, an error of +3 yields a loss three times greater than an error
of -1.
20. Vector autoregressive models should be used for forecasting if the series being studied are
cointegrated.