Câu hỏi: If a series, yt, follows a random walk (with no drift), what is the optimal 1-step ahead forecast for y?

A. The current value of y

B. Zero

C. The historical unweighted average of y

D. An exponentially weighted average of previous values of y

Câu 1: Which of the following sets of characteristics would usually best describe an autoregressive process of order 3 (i.e. an AR(3))?

A. A slowly decaying acf, and a pacf with 3 significant spikes

B. A slowly decaying pacf and an acf with 3 significant spikes

C. A slowly decaying acf and pacf

D.  An acf and a pacf with 3 significant spikes

Câu 2: Consider the following picture and suggest the model from the following list that best characterises the process:

A. An AR(1)

B. An AR(2)

C. An ARMA(1,1)

D. An MA(3)

Câu 3: If there are three variables that are being tested for cointegration, what is the maximum number of linearly independent cointegrating relationships that there could be?

A. 0

B. 1

C. 2

D. 3

Câu 4: If a Johansen “max” test for a null hypothesis of 1 cointegrating vectors is applied to a system containing 4 variables is conducted, which eigenvalues would be used in the test?

A. The largest 1

B. The Second largest

C. The Second smallest

D. The smallest

Câu 5: Which criticism of Dickey-Fuller (DF) -type tests is addressed by stationarity tests, such as the KPSS test?

A. DF tests have low power to reject the null hypothesis of a unit root, particularly in small samples

B.  DF tests are always over-sized

C. DF tests do not allow the researcher to test hypotheses about the cointegrating vector

D. DF tests can only find at most one cointegrating relationship

Câu 6: Consider a series that follows an MA(1) with zero mean and a moving average coefficient of 0.4. What is the value of the autocorrelation function at lag 1?

A. 0.4

B. 0.34

C. 1

D. It is not possible to determine the value of the autocovariances without knowing the disturbance variance