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eee · 2018年06月12日

追问打错字了,重新开贴问下因变量单位根检验问题



eee ·

如何判断因变量是否有单位根?



Finally, Dennehy would like to confirm that nonstationarity is not a problem. To test for this he conducts Dickey–Fuller tests for a unit root on each of the time series. The results are reported in Exhibit 2.




EXHIBIT 2

RESULTS OF THE DICKEY-FULLER TESTS

Time SeriesValue of the Test StatisticStandard Errort-StatisticSignificance oft
Defective assemblies per hour0.00360.00231.5910.1123
Outside air temperature–0.4230.0724–5.8460
Assembly line speed–0.5860.043–13.5100





Q. Assuming a 5% level of significance, the most appropriate conclusion that can be drawn from the Dickey–Fuller results reported in Exhibit 2 is that the:

  1. test for a unit root is inconclusive for the dependent variable.
  2. independent variables exhibit unit roots but the dependent variable does not.
  3. dependent variable exhibits a unit root but the independent variables do not.

Solution

C is correct. The Dickey–Fuller test uses the following type of regression:

xtxt−1 = b0 + g1xt−1 + εt, Et) = 0

The null hypothesis is H0: g1 = 0 versus the alternative hypothesis Ha: g1 < 0 (a one-tail test). If g1 = 0, the time series has a unit root and is nonstationary. Thus, if the null hypothesis fails to be rejected, then the possibility exists that the time series has a unit root and is nonstationary.

Based on the t ratios and their significance levels in Exhibit 2, the null hypothesis that the coefficient is zero is rejected for both outside air temperature and assembly line speed (i.e., the independent variables). But the null hypothesis is not rejected for the dependent variable, defective assemblies per hour.


之前助教回答如下:

和自变量判断方法一样,比如这道题,用DF检验,检验g是否为0,自变量的P值大于0.05,所以是不显著的,因此g=0,有单位根

我还是不明白以下两点:

1、一般说来,g不是检验自变量的吗,而p值大于0.05的是因变量,这之间有什么关系?
2、自变量都是有估计系数的,用系数除以标准差会产生t统计量,因变量本身没有系数估计,value of t以及t 的值是怎么出来的呢?

1 个答案

品职辅导员_小明 · 2018年06月12日

g并不是检验自变量的,我们在这里说的是AR模型,也就是自己和昨天的自己之间的关系,那么Y也可以和昨天的Y组成新的公式做DF检验,组成新的公式,也就有了b1

无论是X还是Y,都是检验g是否为0,也就是b1是否为1

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