Q1. David Wellington, CFA, has estimated the following log-linear trend model: LN(x_t) = b₀ + b₁t + ε_t. Using six years of quarterly observations, 2001:I to 2006:IV, Wellington gets the following estimated equation: LN(x_t) = 1.4 + 0.02t. The first out-of-sample forecast of x_t for 2007:I is closest to:

A)   6.69.

B)   1.88.

C)   4.14.

Q2. Modeling the trend in a time series of a variable that grows at a constant rate with continuous compounding is best done with:

A)    a moving average model.

B)    a log-linear transformation of the time series.

C)    simple linear regression.

Q3. In the time series model: y_t=b₀ + b₁ t + ε_t, t=1,2,…,T, the:

A)     disturbance terms are autocorrelated.

B)     disturbance term is mean-reverting.

C)     change in the dependent variable per time period is b₁.

答案和详解如下：

Q1. David Wellington, CFA, has estimated the following log-linear trend model: LN(x_t) = b₀ + b₁t + ε_t. Using six years of quarterly observations, 2001:I to 2006:IV, Wellington gets the following estimated equation: LN(x_t) = 1.4 + 0.02t. The first out-of-sample forecast of x_t for 2007:I is closest to:

A)   6.69.

B)   1.88.

C)   4.14.

Correct answer is A)

Wellington’s out-of-sample forecast of LN(x_t) is 1.9 = 1.4 + 0.02 × 25, and e^1.9 = 6.69.

Q2. Modeling the trend in a time series of a variable that grows at a constant rate with continuous compounding is best done with:

A)    a moving average model.

B)    a log-linear transformation of the time series.

C)    simple linear regression.

Correct answer is B)

The log-linear transformation of a series that grows at a constant rate with continuous compounding (exponential growth) will cause the transformed series to be linear.

Q3. In the time series model: y_t=b₀ + b₁ t + ε_t, t=1,2,…,T, the:

A)     disturbance terms are autocorrelated.

B)     disturbance term is mean-reverting.

C)     change in the dependent variable per time period is b₁.

Correct answer is C)

The slope is the change in the dependent variable per unit of time. The intercept is the estimate of the value of the dependent variable before the time series begins. The disturbance term should be independent and identically distributed. There is no reason to expect the disturbance term to be mean-reverting, and if the residuals are autocorrelated, the research should correct for that problem.