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不忘初心 · 2024年10月29日

均值回归

NO.PZ2023100703000064

问题如下:

Risk analyst uses data from the HS300 index over the past 260 weeks to estimate the long-term average correlation of the common stocks and mean reverting rate. And find the average long-term stock correlation of the HS 300 Index is 22%, and the regression output estimates the following regression relationship: Y = 0.34-0.55X. Assume that in first week of March 2020, the average weekly correlation of all HS300 stocks was 65%. Based on the mean reverting rate in regression analysis, what is the estimated one-week autocorrelation?

选项:

A.0.219 B.0.23 C.0.35 D.0.45

解释:

To find the estimated one-week autocorrelation based on the mean reverting process, we can use the following formula:



单期自相关率+均值回归率=1,所以自相关率只要拿1减去均值回归率,即1-0.55=0.45

老师好,我还是没太懂,题都没看明白,那两个ρ是指什么,跟题目没关系吗?说的是什么意思呢?如果我们把数据套用St=au+(1-a)st-1,能把题目的数据落到公式上吗?谢谢

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李坏_品职助教 · 2024年10月29日

嗨,从没放弃的小努力你好:


本题的背景是,对美国股市的股票之间的相关系数(correlation)建立回归模型。最后发现 Y = 0.34-0.55X。

这个-0.55表示,相关系数(correlation)的均值回归率是0.55,也就是如果当期的相关系数过高了(显著大于22%了),那么下一期的相关系数会以0.55的速度向22%逼近。


而相关系数除了均值回归的特征之外,还有自相关的特征,也就是有一定的惯性。自相关率+均值回归率=1,所以自相关率 = 1- 0.55 = 0.45.


注意题目说的correlation,是回归模型里面的Y和X,而题目最后问的autocorrelation,指的是自相关率。


如果按照课件例题的写法(例题里面问的是correlation是多少,和你提问的题目问的不一样):

这个例题也有Y和X的关系,可以立刻得出均值回归率是0.75,而自相关率是1-0.75 = 0.25.

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

不忘初心 · 2024年10月29日

谢谢老师,很详细的讲解,我好像明白点了。我多看几遍讲解,再体会下。谢谢老师!

李坏_品职助教 · 2024年10月29日

嗨,从没放弃的小努力你好:


继续加油!!

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ2023100703000064 问题如下 Risk analyst uses ta from the HS300 inx over the past 260 weeks to estimate the long-term average correlation of the common stocks anmereverting rate. Anfinthe average long-term stocorrelation of the HS 300 Inx is 22%, anthe regression output estimates the following regression relationship: Y = 0.34-0.55X. Assume thin first week of Mar2020, the average weekly correlation of all HS300 stocks w65%. Baseon the mereverting rate in regression analysis, whis the estimateone-week autocorrelation? A.0.219 B.0.23 C.0.35 0.45 To finthe estimateone-week autocorrelation baseon the mereverting process, we cuse the following formula:单期自相关率+均值回归率=1,所以自相关率只要拿1减去均值回归率,即1-0.55=0.45 答案里说 均值回归项的系数是0.55,所以自相关系数就是1-0.55=0.45那为什么 均值回归项不能是0.34 呢?S(t+1)= + (1-a)S(t) 不也是均值回归项在前面吗?

2024-08-07 21:00 1 · 回答

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