问一道题：NO.PZ2018101001000058

问题如下：

Tom wants to predict the income of his factory in October 20X9, so he uses income of January 20X6 to September 20X9 as samples to make a AR(1) model and gets the following result: ${\widehat{X}}_t$ =293.5742+0.9387X_t-1.

If given the income of September 20X9 is $4957.63, based on the mean-reverting level, the predicted income of the factory in October 20X9 is most likely to be:

选项：

more than September’s income.

equal to September’s income.

less than September’s income.

解释：

C is correct.

考点：Covariance-stationary series and mean reversion.

解析：根据题目中给定的AR(1)方程，可以得到b₀=293.5742，b₁=0.9387，就可以计算均值复归水平${\widehat{X}}_t=\frac{b_0}{1-b_1}=\frac{293.5742}{1-0.9387}=\$4789.1387$ 。因为九月的收入为$4957.63大于均值复归水平，所以预计十月的收入会小于九月的收入。选择C选项。