Exam Questions | Regression With Time-Series Data – Ch.9

File: Chapter 9 – Regression with Time-Series Data: Stationary Variables

Multiple Choice

1. Which of the following is an example of a distributed lag model?

a. y_t = f(x_t, x_t-1, x_t-2…….)

b. y_t = f(y_t-1, x_t, x_t-1, x_t-2…)

c. y_t = f(x_t, x²_t, x³_t)

d. y_t = f(x_t) + g(e_t-1)

Ans. a

Level: Easy – Knowledge

AACSB: Reflective Thinking

Section: 9.1

2. Which of the following is an example of an autoregressive distributed lag model?

a. y_t = f(x_t, x_t-1, x_t-2…….)

b. y_t = f(y_t-1, x_t, x_t-1, x_t-2…)

c. y_t = f(x_t, x²_t, x³_t)

d. y_t = f(x_t) + g(e_t-1)

3. Which model below has an autocorrelated error term?

a. y_t = f(x_t, x_t-1, x_t-2…….)

b. y_t = f(y_t-1, x_t, x_t-1, x_t-2…)

c. y_t = f(x_t, x²_t, x³_t)

d. y_t = f(x_t) + g(e_t-1)

4. Which assumption is most likely to be violated with times series data?

a.) E(e_t)=0

b.) var (e_t)=²

c.) cov(e_t, e_s) =0, t≠s

d.) e_t N(0,²)

5. What is second order sample autocorrelation?

a. Correlation between a mean and the second moment of the sample distribution

b. A test statistic distributed N(0,)

c. Correlation between observations that are two time-periods apart

d. Correlation between the dependent variable and a squared explanatory variable

6. Using the notation ARDL(p,q) what does p represent?

a. The number of lagged dependent variables included as explanatory variables

b. The number of lagged explanatory variables included

c. The frequency of the time series

d. The degree or integration in the error term

7. Using the notation ARDL(p,q) what does q represent?

a. The number of lagged dependent variables included as explanatory variables

b. The number of lagged explanatory variables included

c. The frequency of the time series

d. The degree or integration in the error term

8. Which of the following is an ARDL(1,3) model?

a. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

b. y_t = + ₁y_t-1+ ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

c. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+ v_t

d. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + v_t

9. Which of the following is an AR(3) model?

a. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

b. y_t = + ₁y_t-1+ ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

c. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+ v_t

d. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + v_t

10. Which of the following is an ARDL(3,3) model?

a. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

b. y_t = + ₁y_t-1+ ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

c. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+ v_t

d. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + v_t

11. Which of the following is an ARDL(2,0) model?

a. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

b. y_t = + ₁y_t-1+ ₀x_t + ₁x_t-1+₂x_t-2+ ₃x_t-3 + v_t

c. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + ₁x_t-1+ v_t

d. y_t = + ₁y_t-1+₂y_t-2 +₃y_t-3 + ₀x_t + v_t

12. If we wish to test to see whether an s-order sample autocorrelation is significantly different from zero at a 5% significant level, then a test statistic that is suitable is _____.

a.

b.

c.

d.

13. When the assumption of stationary variables is used, which of the following statements about expected mean and expected variance are being assumed as TRUE?

a. Only the expected mean remains constant over time.

b. Only the expected variance remains constant over time.

c. Both the expected mean and expected variance remain constant over time.

d. The expected mean and expected variance are a linear function of time.

14. Finite distributed lag models are most useful for _____.

a. forecasting and economic policy analysis

b. testing hypotheses and measuring economic dynamics

c. measuring impacts and optimizing economic outcomes

d. measuring autocorrelation and autoregressive dynamics

15. If you use a times series data set with 100 years’ worth of data to estimate a distributed lag model of order 5, how many observations will you have for estimation?

a. 100

b. 5

c. 95

d. 105

16. AR models are primarily used for _____.

a. forecasting

b. smoothing data over time

c. policy evaluation

d. hypothesis testing

17. Which of the following is not a valid criterion for choosing p and q in an ARDL model?

a. Fewest number of lags that eliminates serial correlation

b. Statistical significance of coefficient estimates

c. Minimization of AIC and SC

d. Maximization of R²

18. When using the LM test for serial correlation, what is the null hypothesis?

a.) It depends on the model specification.

b.) No serial correlation is present.

c.) Statistically significant serial correlation with the first lag.

d.) Statistically significant serial correlation with unspecified lag.

19. When performing a LM test for serial correlation, how is the test statistic distributed when the null hypothesis is true?

a.) ²

b.) t_n-1

c.) F

d.) z

20. How do you calculate the total multiplier for a finite distributed lag model where q is the number of lags?

a. _q

b.

c.

d. _q-₀

21. Which of the following is NOT true of Newey-West standard errors?

a. Allows valid inference despite the presence of serial correlation

b. Does not require knowledge of structure of serial correlation

c. Valid when estimated using stationary data

d. Always produce smaller standard error estimates, which makes them the BLUE estimator

22. Which of the following is NOT a reason nonlinear least squares is used to estimate an AR(1) model?

a. Linear least squares is not possible since the transformation that allows the new error term to be uncorrelated is no longer linear in parameters.

b. Using OLS to estimate the untransformed model provides incorrect standard errors.

c. The algorithmic nonlinear optimization is less complicated to compute when error terms are correlated.

d. Minimizing the sum of squares of uncorrelated error terms produces an estimator that is unbiased and consistent.

23. How do you calculate the total multiplier for an infinite distributed lag model with geometrically declining lags?

a.

b.

c.

d.

24. Which of the following is equivalent to L³y_t?

a. y _t-3

b. 3L² y _t

c. Ly_t L²y_t

d. Ly³_t

25. Show how a standard AR(1) error model can be rewritten as an ARDL(1,1) model.

2. Solve the y_t equation for e_t, lag the equation by one period and multiply by :

3. Substitute equation into the y_t equation from step 1. And rearrange:

4. Let :

Level: Medium – Application

AACSB: Analytical

Section 9.1

26. In the context of forecasting, explain what Granger causality means.