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dejiazheng · 2023年12月10日

可否理解为t=0.4504<critical value1.98,接受H0:b1=1,说明有单位根现象

* 问题详情,请 查看题干

NO.PZ201709270100000503

问题如下:

3.Based on the regression results in Exhibit 1, the original time series of exchange rates:

选项:

A.

has a unit root.

B.

exhibits stationarity.

C.

can be modeled using linear regression.

解释:

A is correct. If the exchange rate series is a random walk, then the first-differenced series will yield b0 = 0 and b1 = 0, and the error terms will not be serially correlated. The data in Exhibit 1 show that this is the case: Neither the intercept nor the coefficient on the first lag of the first-differenced exchange rate in Regression 2 differs significantly from zero because the t-statistics of both coefficients are less than the critical t-statistic of 1.98. Also, the residual autocorrelations do not differ significantly from zero because the t-statistics of all autocorrelations are less than the critical t-statistic of 1.98. Therefore, because all random walks have unit roots, the exchange rate time series used to run Regression 1 has a unit root.

请老师指正

Phoebe · 2024年03月24日

Why all random walk has unit root?

3 个答案

品职助教_七七 · 2024年03月24日

嗨,爱思考的PZer你好:


@Phoebe

1)unit root和random walk是同义词,对应的都是b1=1;

2)根据regression 2的检验结果,可知regression 2的b0和b1都为0,regression 2进而化简为yt=εt。由于yt=Xt-Xt-1,所以Xt-Xt-1=εt。也就是Xt序列(the original time series)是random walk。

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Phoebe · 2024年03月24日

  那如果不能通过regression 2 里b1=0 来反推出原时间序列数据里b1=1 的结论,怎么来判断原数据是有单位根的呢?

品职助教_七七 · 2023年12月10日

嗨,从没放弃的小努力你好:


不可以,

t=0.4504这个结果对应的是regression 2的方程:

所以,t=0.4504<1.98可以得到的结论为:不拒绝regression 2中的H0:b1=0。也就是regression 2中的b1=0。

注意:

1)此处为regression 2中b1是否为0的结论,不是b1是否为1的结论。

2)这个b1和regression 1中的b1不是同一个值。结论也不能混用。无法通过对于regression 2的假设检验,来得到关于regression 1中的b1是否为1的结论。


如果想检验regression 1中的b1,需要对regression 1,也就是如下方程重新发起检验:

由于题干中未给关于regression 1的检验结果,所以这条路走不通,不能直接得到b1。只能通过答案解析的方法,通过regression 2,曲线的来得到这个方程中的b1=1.


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2024-11-01 21:02 1 · 回答

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2024-05-05 11:27 1 · 回答

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