Q1. An analyst wants to model quarterly sales data using an autoregressive model. She has found that an AR(1) model with a seasonal lag has significant slope coefficients. She also finds that when the second and third lags are added to the model, all slope coefficients are significant too. Based on this, the best model to use would most likely be an:

A)   AR(1).

B)   AR(4).

C)   AR(2).

Q2. The model x_t = b₀ + b₁ x_t-1 + b₂ x_t-2 + b₃ x_t-3 + b₄ x_t-4 + ε_t is:

A)     an autoregressive conditional heteroskedastic model, ARCH.

B)     an autoregressive model, AR(4).

C)     a moving average model, MA(4).

Q3. The model x_t = b₀ + b₁ x_{t − 1} + b₂ x_{t − 2}  + ε_t is:

A)     an autoregressive conditional heteroskedastic model, ARCH.

B)     an autoregressive model, AR(2).

C)     a moving average model, MA(2).

答案和详解如下：

Q1. An analyst wants to model quarterly sales data using an autoregressive model. She has found that an AR(1) model with a seasonal lag has significant slope coefficients. She also finds that when the second and third lags are added to the model, all slope coefficients are significant too. Based on this, the best model to use would most likely be an:

A)   AR(1).

B)   AR(4).

C)   AR(2).

Correct answer is B)

She has found that all the slope coefficients are significant in the model x_t = b₀ + b₁x_t–1 + b₂x_t–4 + e_t. She then finds that all the slope coefficients are significant in the model x_t = b₀ + b₁x_t–1 + b₂x_t–2 + b₃x_t–3 + b₄x_t–4 + e_t. Thus, the second model, the AR(4), should be used over the first or any other model that uses a subset of the regressors.

Q2. The model x_t = b₀ + b₁ x_t-1 + b₂ x_t-2 + b₃ x_t-3 + b₄ x_t-4 + ε_t is:

A)     an autoregressive conditional heteroskedastic model, ARCH.

B)     an autoregressive model, AR(4).

C)     a moving average model, MA(4).

Correct answer is B)

This is an autoregressive model (i.e., lagged dependent variable as independent variables) of order p=4 (that is, 4 lags).

Q3. The model x_t = b₀ + b₁ x_{t − 1} + b₂ x_{t − 2}  + ε_t is:

A)     an autoregressive conditional heteroskedastic model, ARCH.

B)     an autoregressive model, AR(2).

C)     a moving average model, MA(2).

Correct answer is B)

This is an autoregressive model (i.e., lagged dependent variable as independent variables) of order p = 2 (that is, 2 lags).