问一道题：NO.PZ2015120204000054

问题如下：

Maxwell recognizes that annual gross revenue for a property depends on the nightly room rate and the occupancy rate. She believes that the primary driver for the nightly room rate is the Employment Cost Index (ECI) and that the primary driver for the occupancy rate is the Consumer Sentiment Index (CSI). In the process of simulating revenues, she examines the ECI and the CSI quarterly over the past 20 years and their relation to the nightly room rate and occupancy rates of the REIT’s existing properties, respectively. She estimates the following:
Nightly room rate = $23 + 0.9(ECIt–1)
Occupancy rate = 0.25 + 0.7(CSIt–1)
Occupancy rates are assumed to be non-negative and cannot exceed 100%.

Maxwell generates 10,000 trials of the ECI and CSI based on the historical mean level of the indexes and their monthly standard deviations. Although the distribution of historical CSI is not symmetric, she assumes that both ECI and CSI are normally distributed. Maxwell is aware that if the inputs are correlated, this may present a problem. She also observes that the CSI and the ECI are correlated with one another and that the relation between the CSI and the occupancy rate is stronger than that between the ECI and nightly room rates. Maxwell estimates the corresponding nightly room rate and the occupancy rate based on these historical relations, multiplies these by the number of hotel nights in a year, and generates 10,000 estimates of annual gross revenue.

With respect to forecasting annual gross revenue, Maxwell’s best course of action to deal with the inputs problem should be to:

选项：

simulate the ECI and the CSI independently.

build the correlation explicitly into the simulation.

estimate revenues using the ECI only and eliminate the CSI from the simulation.

解释：

B is correct. Both the nightly room rate and the occupancy rate are dependent on inputs, ECI and CSI, which are correlated. If there are correlated inputs, there are two solutions to this problem. One is to allow only one of the two inputs to vary, emphasizing the one with the larger impact. The second solution is to the build the correlation explicitly into the simulation. Simulating ECI and CSI independently is not a remedy for the correlated inputs problem. Further, the relation between CSI and the occupancy rate is stronger than that between ECI and nightly room rates, which suggests that CSI should be kept if one of the two inputs is to be removed from the simulation. A is incorrect because the two input variables, ECI and CSI, are correlated, and simulating them independently is not appropriate. The remedies include dropping one of the probabilistic inputs or building the correlation into the simulation explicitly. C is incorrect because the relation between CSI and the occupancy rate is stronger than that between ECI and nightly room rates, which suggests that CSI should be kept if one of the two inputs is to be removed from the simulation