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: 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 2: If a residual series is negatively autocorrelated, which one of the following is the most likely value of the Durbin Watson statistic?

A. Close to zero

B. Close to two

C. Close to four

D. Close to one

Câu 3: What would be the consequences for the OLS estimator if autocorrelation is present in a regression model but ignored?

A. It will be biased

B. It will be inconsistent

C. It will be inefficient

D. All of a, b and c will be true

Câu 4: 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 5: 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 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