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Spencer · 2020年02月21日

问一道题：NO.PZ201709270100000405

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

问题如下：

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

X∧t+1=b^0+b^1Xt+b^2Xt−1{\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

X∧t+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.

老师请问，这题和这一case的第一小题中求 predicted WTI oil price for October 2015 using the linear trend model, t 用183代入，这里的Oil Price aug 2015就不用181，Oil Price July 2015就不用180带入？

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星星_品职助教 · 2020年02月21日

同学你好，

linear trend model是线性回归模型，所以可以把时间值当做一个变量

而这道题是“AR”模型，AR的核心是用昨天的我来解释今天的我，所以代入的不是时间值，而是Xt-1，Xt-2...来解释Xt

 

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NO.PZ201709270100000405 $40.04. $61.77. B is correct. The last two observations in the WTI time series are July anAugust 2015, when the WTI oil priw$51.16 an$42.86, respectively. Therefore, September 2015 represents a one-perioaheforecast. The one-perio aheforecast from AR(2) mol is calculateX∧t+1=b^0+b^1Xt+b^2Xt−1{\overset\wee X}_{t+1}={\wihb}_0+{\wihb}_1X_t+{\wihb}_2X_{t-1}X∧t+1​=b 0​+b 1​Xt​+b 2​Xt−1​ So, the one-perioahe(September 2015) forecast is calculateX∧t+1=2.0017+1.3946($42.86)−0.4249($51.16)=$40.04{\overset\wee X}_{t+1}=2.0017+1.3946(\$42.86)-0.4249(\$51.16)=\$40.04X∧t+1​=2.0017+1.3946($42.86)−0.4249($51.16)=$40.04 Therefore, the September 2015 forecast baseon the AR(2) mol 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stanerror那一项数字5·2799给加上了。谢谢老师啦，辛苦

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