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reachqi · 2019年11月05日

问一道题:NO.PZ201709270100000503

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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.

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. 如果原始数据存在单位根,那么它的一阶差分也就是 Regression 2中的B0和B1都会等于0,并且不存在自相关。可是为什么呢?为什么原始数据存在单位根,那它的一阶差分也就是 Regression 2中的B0和B1都会等于0???

1 个答案
已采纳答案

星星_品职助教 · 2019年11月05日

同学你好,

分几步来说哈,首先先不考虑“差分”的问题,就从yt和yt-1的角度考虑,这样是一个简单的AR(1)模型,分析起来容易一些。

由于b0和b1的t统计量都很小,所以都无法拒绝等于0的原假设。也就是可以简单理解为假设检验的结果就是b0=0,b1=0,这个时候AR(1)模型其实就退化为了yt=εt。

这个时候再回头考虑原始数据,由于yt=Xt – Xt-1,所以这个模型就可以转化为Xt – Xt-1=εt,即Xt =Xt-1 +εt,这个时候就可以很明显的看出在这个X的时间序列里,Xt-1前的系数为1,即有单位根现象。

这道题老师上课详细的讲过的,所以建议先听视频再做题哈。即使知识点已经会了,再听视频对于整体框架的理解和这个知识点逻辑上与前后知识点的关联也会有帮助~ 加油~

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