Q1. David Brice, CFA, has used an AR(1) model to forecast the next period’s interest rate to be 0.08. The AR(1) has a positive slope coefficient. If the interest rate is a mean reverting process with an unconditional mean, a.k.a., mean reverting level, equal to 0.09, then which of the following could be his forecast for two periods ahead?

A)   0.113.

B)   0.081.

C)   0.072.

Q2. Which of the following statements regarding a mean reverting time series is FALSE?

A)     If the current value of the time series is above the mean reverting level, the prediction is that the time series will increase.

B)     If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease.

C)     If the time-series variable is x, then x_t = b₀ + b₁ x_t.

Q3. Suppose that the time series designated as Y is mean reverting. If Y_t+1 = 0.2 + 0.6 Y_t, the best prediction of Y_t+1 is: A)         0.3.

B)     0.8.

C)     0.5.

答案和详解如下：

Q1. David Brice, CFA, has used an AR(1) model to forecast the next period’s interest rate to be 0.08. The AR(1) has a positive slope coefficient. If the interest rate is a mean reverting process with an unconditional mean, a.k.a., mean reverting level, equal to 0.09, then which of the following could be his forecast for two periods ahead?

A)   0.113.

B)   0.081.

C)   0.072.

Correct answer is B)

As Brice makes more distant forecasts, each forecast will be closer to the unconditional mean. So, the two period forecast would be between 0.08 and 0.09, and 0.081 is the only possible answer.

Q2. Which of the following statements regarding a mean reverting time series is FALSE?

A)     If the current value of the time series is above the mean reverting level, the prediction is that the time series will increase.

B)     If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease.

C)     If the time-series variable is x, then x_t = b₀ + b₁ x_t.

Correct answer is A)

If the current value of the time series is above the mean reverting level, the prediction is that the time series will decrease; if the current value of the time series is below the mean reverting level, the prediction is that the time series will increase.

Q3. Suppose that the time series designated as Y is mean reverting. If Y_t+1 = 0.2 + 0.6 Y_t, the best prediction of Y_t+1 is: A)         0.3.

B)     0.8.

C)     0.5.

Correct answer is C)

The prediction is Y_t+1 = b₀ / (1-b₁) = 0.2 / (1-0.6) = 0.5