Q1. Alexis Popov, CFA, is analyzing monthly data. Popov has estimated the model x_t = b₀ + b₁ × x_t-1 + b₂ × x_t-2 + e_t. The researcher finds that the residuals have a significant ARCH process. The best solution to this is to:

A)   re-estimate the model with generalized least squares.

B)   re-estimate the model using only an AR(1) specification.

C)   re-estimate the model using a seasonal lag.

Q2. Alexis Popov, CFA, has estimated the following specification: x_t = b₀ + b₁ × x_t-1 + e_t. Which of the following would most likely lead Popov to want to change the model’s specification?

A)   Correlation(e_t, e_t-1) is not significantly different from zero.

B)   Correlation(e_t, e_t-2) is significantly different from zero.

C)   b₀ < 0.

Q3. Alexis Popov, CFA, wants to estimate how sales have grown from one quarter to the next on average. The most direct way for Popov to estimate this would be:

A)   an AR(1) model.

B)   a linear trend model.

C)   an AR(1) model with a seasonal lag.

答案和详解如下：

Q1. Alexis Popov, CFA, is analyzing monthly data. Popov has estimated the model x_t = b₀ + b₁ × x_t-1 + b₂ × x_t-2 + e_t. The researcher finds that the residuals have a significant ARCH process. The best solution to this is to:

A)   re-estimate the model with generalized least squares.

B)   re-estimate the model using only an AR(1) specification.

C)   re-estimate the model using a seasonal lag.

Correct answer is A)

If the residuals have an ARCH process, then the correct remedy is generalized least squares which will allow Popov to better interpret the results.

Q2. Alexis Popov, CFA, has estimated the following specification: x_t = b₀ + b₁ × x_t-1 + e_t. Which of the following would most likely lead Popov to want to change the model’s specification?

A)   Correlation(e_t, e_t-1) is not significantly different from zero.

B)   Correlation(e_t, e_t-2) is significantly different from zero.

C)   b₀ < 0.

Correct answer is B)

If correlation(e_t, e_t-2) is not zero, then the model suffers from 2^nd order serial correlation. Popov may wish to try an AR(2) model. Both of the other conditions are acceptable in an AR(1) model.

Q3. Alexis Popov, CFA, wants to estimate how sales have grown from one quarter to the next on average. The most direct way for Popov to estimate this would be:

A)   an AR(1) model.

B)   a linear trend model.

C)   an AR(1) model with a seasonal lag.

Correct answer is B)

If the goal is to simply estimate the dollar change from one period to the next, the most direct way is to estimate x_t = b₀ + b₁ × (Trend) + e_t, where Trend is simply 1, 2, 3, ....T. The model predicts a change by the value b₁ from one period to the next.