Câu hỏi: If the residuals of a model containing lags of the dependent variable are autocorrelated, which one of the following could this lead to?

A. Biased but consistent coefficient estimates

B. Biased and inconsistent coefficient estimates

C. Unbiased but inconsistent coefficient estimates

D. Unbiased and consistent but inefficient coefficient estimates

Câu 1: 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 2: 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 3: 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 4: Which of the following would probably NOT be a potential “cure” for non-normal residuals?

A. Transforming two explanatory variables into a ratio

B. Removing large positive residuals

C. Using a procedure for estimation and inference which did not assume normality

D. Removing large negative residuals

Câu 5: 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 6: Which of the following conditions must hold for the autoregressive part of an ARMA model to be stationary?

A. All roots of the characteristic equation must lie outside the unit circle

B. All roots of the characteristic equation must lie inside the unit circle

C. All roots must be smaller than unity

D. At least one of the roots must be bigger than one in absolute value