问一道题：NO.PZ2018101001000056

问题如下：

Smith wants to help his friend Jenny to predict the income of his shop in October 20X9 , so he uses income of January 20X6 to September 20X9 as samples to make a AR(2) model and gets the following result: ${\widehat{X}}_{t+1}$ =1.3458+0.8912X_t+0.3372X_t-1.What is the predicted income of Jenny’s shop in October 20X9 if given the income of August 20X9 is $2746.72 and the income of September 20X9 is $2957.63?

选项：

$3446.54

$3563.38

$3678.42

解释：

B is correct.

考点: Introduction of AR & Chain Rule of Forecasting.

解析: 对于本题来说，当我们用AR(2)模型来预测下个月店铺的收入时，我们需要依次代入前两个月的数据，X_t对应九月的收入，X_t-1对应八月的收入。

${\widehat{X}}_{t+1}$ =1.3458+0.8912($2957.63)+0.3372($2746.72)=$3563.38，选择B选项。