Briefly explain how to test for non-stationarity in a time series using the Dickey-Fuller test.

Assignment 1:

Part A

A1.An AR(2) process has a characteristic equation with two roots: z=-3 and z=1. What can you say about this series?

a. The series is stationary.

b. The series is non-stationary. It contains one unit root.

c. The series is non-stationary. It contains two unit roots.

d. The series is I(0).

A2. Which of the following statements is correct?

a. A stationary AR(1) model has a PACF which is significant for lag 1 and insignificant for other lags.

b. A non-stationary AR(1) model has an ACF which is significant for lag 1 and insignificant for other lags.

c. An MA(1) model has a PACF which is significant for lag 1 and insignificant for other lags.

d. A stationary AR(1) model has a PACF that decays geometrically.

A3. Among the following tests, which one is typically used to detect serial correlation in the residuals of a regression?

a. KPSS test.

b. Durbin-Watson test.

c. Phillips-Perron test.

d. None of the above.

A4. You have downloaded from Datastream historical share price data for a company. Which among of the following tests would be useful to understand whether the series is stationary or non-stationary?

a. Augmented Dickey-Fuller test.

b. Breusch-Godfrey test.

c. Durbin-Watson test.

d. None of the above.

A5. The time series y(t) must be differenced once in order to achieve a stationary transformation. We can say that:

a. The series is I(0).

b. The series is I(2), or integrated of order 2.

c. The series contains two unit roots.

d. None of the above.

A6. Which of the following statements is correct?

a. The product of a 2 x 5 matrix by a 5 x 3 matrix is a 2 x 3 matrix.

b. The product of a 5 x 2 matrix by a 3 x 5 matrix is a 2 x 3 matrix.

c. The product of a 2 x 5 matrix by a 5 x 3 matrix is not defined.

d. None of the above.A7. What is the trace of the square matrix: A =

a. 6.
b. 5.
c. 12.

d. None of the above.

A8. You have to write the characteristic equation of the AR(2) process:

yt = 0.5yt-1 + 0.4yt-2 + ut

Which of the following equations is correct?

a. 1 + 0.6z - 0.3z2 = 0

b. 1 + 0.5z + 0.4z2 = 0

c. 1 - 0.5z - 0.4z2 = 0

d. None of the above.

A9. Which of the following statements about the Durbin-Watson test is correct?

a. There must be a constant term in the regression.

b. There must be no lags of the dependent variable in the regression (it should not be a dynamic model).

c. The Durbin-Watson statistic does not follow a Chi-square distribution.

d. All of the above statements are correct.

A10. You have run four bivariate Vector Autoregression (VAR) models, with 2, 3, 4, and 5 lags, respectively. The computed values for the Multivariate Akaike Information Criteria are as follows:

Lag MAIC

2 -17.844

3 -17.901

4 -18.856

5 -17.852

Which model would you prefer?

a. The model with 2 lags.

b. The model with 3 lags.

c. The model with 4 lags.

d. The model with 5 lags.

Question A-ii. Give a short definition of endogeneity

Part B:

B1. Explain the concept of cointegration in the context of spot and futures prices of a commodity. How could you test for cointegration using the Engle-Granger approach?

B2. Briefly explain how to test for non-stationarity in a time series using the Dickey-Fuller test.

B3. Explain the concept of spurious regression in the context of models with non-stationary time series.

B4. Briefly describe the Breusch-Godfrey (BG) test for serial correlation in the residuals of a regression.

B5. Explain how you can choose between a Random Effect and a Fixed Effect (also Within-Group) model using a Hausman test. If the Hausman test is rejected, what can you conclude?

B6. Briefly describe the main features of a Moving Average process and of an Autoregressive process.

B7. Compare the standard GARCH(1,1) model with the GJR-GARCH(1,1) model.

B8. Briefly discuss Vector Autoregression models.

Assignment 2:

Part A
A1. Which of the following is not a necessary assumption underlying Ordinary Least Squares (OLS) estimation of the coefficients of a linear regression?

A. The error term is random.

B. The explanatory variable is endogenous.

C. The error term is homoscedastic.

D. The error term is normally distributed.

E. Both B and D.

A2. In the estimation of a two-variable linear regression model using 20 observations, a researcher has obtaine? ^2 = 3.34 and se(? ^2) = 1.86. Which of the following is TRUE?

A. is significantly greater than zero in a one-tail test at the 0.05 significance level.

B. is significantly different from zero in a two-tail test at the 0.05 significance
level.

C. The p-value for a test of H0:?2=0 against H1:?2>0 is smaller than 0.01.

D. The p-value for a test of H0:?2=0 against H1:?2?0 is larger than 0.1.

E. Both B and D.

A3. You have fitted a cross-sectional regression using n=30 observations, and you have then estimated an auxiliary regression of the squared residuals on the squared fitted values. The R2 value in the auxiliary regression is 0.16. What do you infer from this result?

A. The residuals from the cross-sectional regression are homoscedastic.

B. The residuals from the cross-sectional regression are free of serial correlation.

C. The residuals from the cross-sectional regression are not normally distributed.

D. The residuals from the cross-sectional regression are heteroscedastic.

E. The residuals from the cross-sectional regression are serially correlated.