问一道题：NO.PZ2018101001000064

问题如下：

White wants to predict the income of his factory in the first quarter of 20X9, so he uses income in the first quarter of 20X4 to the last quarter of 20X8 as samples to make a AR(1) model but finds in the autocorrelations of the residual table that there is a strong and significant seasonal autocorrelation. Then he corrects the model and gets the new model which is X ^ t =126.7537+0.1387Xt-1+0.9324Xt-4. The following table shows the quarter income in 20X8:

What is the predicted income of his factory in the first quarter of 20X9 if based on this new model?

选项：

4895.9543

5938.4207

6091.0998

解释：

C is correct.

考点: Seasonality.

解析：由得到的新公式可以知道，为了预测工厂20X9年第一季度的收入，我们需要代入滞后一项及滞后四项的数据，即20X8年第四季度的数据和20X8年第一季度的数据。 ${\widehat{X}}_t$ =126.7537+0.1387X_t-1+0.9324X_t-4

=126.7537+0.1387*($4257.63) + 0.9324*($5763.42) =$6091.0998