6.Using the log-linear trend model, the forecast of sales for Very Vegan for the first out-of-sample period is:

A)   $109.4 million.

B)   $121.2 million.

C)   $117.0 million.

D)   $107.8 million.

The correct answer was C)

The forecast is e^{2.9803 + (13 × 0.1371)} = 117.01.

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

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

B)   dependent variable is meaningless.

C)   disturbance term is mean-reverting.

D)   disturbance terms are autocorrelated.

The correct answer was A)

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.

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

A)   simple linear regression.

B)   a moving average model.

C)   a mean reversion model.

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

The correct answer was D)     

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.

9．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)   1.88.

B)   6.69.

C)   1.70.

D)   4.14.

The correct answer was B)

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