开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

山风泽笑 · 2021年05月10日

残差项et为何不加?

* 问题详情,请 查看题干

NO.PZ201709270100000405

问题如下:

Angela Martinez, an energy sector analyst at an investment bank, is concerned about the future level of oil prices and how it might affect portfolio values. She is considering whether to recommend a hedge for the bank portfolio’s exposure to changes in oil prices. Martinez examines West Texas Intermediate (WTI) monthly crude oil price data, expressed in US dollars per barrel, for the 181-month period from August 2000 through August 2015. The end-of-month WTI oil price was $51.16 in July 2015 and $42.86 in August 2015 (Month 181). After reviewing the time-series data, Martinez determines that the mean and variance of the time series of oil prices are not constant over time. She then runs the following four regressions using the WTI time-series data.

Ÿ Linear trend model: Oil pricet = b0 + b1t+ et

Ÿ Log-linear trend model: ln Oil pricet = b0 + b1t+ et

Ÿ AR(1) model: Oil pricet = b0 + b1Oil pricet1 + et

Ÿ AR(2) model: Oil pricet = b0 + b1Oil pricet1 + b2Oil pricet2 + et

Exhibit 1 presents selected data from all four regressions, and Exhibit 2 presents selected autocorrelation data from the AR(1) models.

In Exhibit 1, at the 5% significance level, the lower critical value for the DurbinWatson test statistic is 1.75 for both the linear and log-linear regressions.

After reviewing the data and regression results, Martinez draws the following conclusions.

Conclusion 1: The time series for WTI oil prices is covariance stationary.

Conclusion 2: Out-of-sample forecasting using the AR(1) model appears to be more accurate than that of the AR(2) model.


5. Based on Exhibit 1, the forecasted oil price in September 2015 based on the AR(2) model is closest to:

选项:

A.

$38.03.

B.

$40.04.

C.

$61.77.

解释:

B is correct. The last two observations in the WTI time series are July and August 2015, when the WTI oil price was $51.16 and $42.86, respectively. Therefore, September 2015 represents a one-period-ahead forecast. The one-period- ahead forecast from an AR(2) model is calculated as

Xt+1=b^0+b^1Xt+b^2Xt1{\overset\wedge X}_{t+1}={\widehat b}_0+{\widehat b}_1X_t+{\widehat b}_2X_{t-1}

So, the one-period-ahead (September 2015) forecast is calculated as

Xt+1=2.0017+1.3946($42.86)0.4249($51.16)=$40.04{\overset\wedge X}_{t+1}=2.0017+1.3946(\$42.86)-0.4249(\$51.16)=\$40.04

Therefore, the September 2015 forecast based on the AR(2) model is $40.04.

请问按照题目里给的公式,最后一项残差项et为何没有加上,我是按照stand error那一项数字5·2799给加上了。谢谢老师啦,辛苦
1 个答案

星星_品职助教 · 2021年05月10日

同学你好,

所有的“predict Y”的考点,都不用加残差值。

预测(predict/forecast/expect)Y值,相当于求的是E(Y),

以本题为例,相当于求E(Oil pricet ),方程两边同时取“E”,可得:

E(Oil pricet )= E(b0 + b1Oil pricet–1 + b2Oil pricet–2) +E( et)

根据方程假设,E( et)=0,所以这一项是直接消掉的。

最后的结果就是E(Oil pricet )= b0 + b1Oil pricet–1 + b2Oil pricet–2。其中b0, b1,Oil pricet–1,b2,Oil pricet–2这些都是给出的数字,代入方程求得E(Oil pricet )即可。