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丁洁Amy · 2021年05月19日

题目图表看不懂

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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.

老师好,


我看这道题的图表看了半天没看明白。表的标题明明是说AR(1)但是表的内容里面又涉及Xt-1 - Xt-2,这不是AR2了么?谢谢老师

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已采纳答案

星星_品职助教 · 2021年05月20日

同学你好,

表的标题说的是这是AR(1)模型的一阶差分(First-Differenced)形式。

原AR(1)方程为:

①AR(1):Xt=b0+b1Xt-1+ε.

一阶差分是把所有的X都往后错一项,方程形式变为:

②First-Differenced:Xt - Xt-1=b0+b1(Xt-1 - Xt-2)+ε

对比AR(2)方程的形式:

③AR(2):Xt=b0+b1Xt-1+b2Xt-2 +ε.

对比这三个方程即可发现差异。


丁洁Amy · 2021年05月20日

謝謝老師,講的很清晰。

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