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EVA · 2024年11月09日

这题是真不明白,说建了一个ARCH2模型,要检验ARCH1的?

NO.PZ2024082801000022

问题如下:

Question An analyst estimates an AR(2) model for the monthly sales of a company and calculates the squared residuals from this regression. To test for the presence of ARCH(1) in the residuals, the analyst should regress the squared residuals on a constant and:

选项:

A.A.a time trend, and test whether the time trend coefficient is statistically different from 0.

B.B.one lag of the squared residuals, and test whether the slope coefficient is statistically different from 0.

C.C.one lag of the squared residuals, and test whether the slope coefficient is statistically different from 1.

解释:

  • A is Incorrect because, to test for ARCH(1), we do the following: Regress the squared residual from your time-series model on a lagged value of the squared residual. Test whether the coefficient on the squared lagged residual differs significantly from 0. So, the independent variable is one lag of the squared residuals, not a time trend.

  • B is Correct because, to test for ARCH(1), we do the following: Regress the squared residual from your time-series model on a lagged value of the squared residual and test whether the coefficient on the squared lagged residual differs significantly from 0.

  • C is Incorrect because, to test for ARCH(1), we do the following: Regress the squared residual from your time-series model on a lagged value of the squared residual. Test whether the coefficient on the squared lagged residual differs significantly from 0. So, the time series has an ARCH(1) process if the slope coefficient is statistically significantly different from 0, not 1.

具体的知识点是哪一个视频

1 个答案

品职助教_七七 · 2024年11月09日

嗨,爱思考的PZer你好:


这个模型是AR(2),不是ARCH(2)。

ARCH(1)是对AR(2)模型的残差项进行的检验,后续分析和AR(2)就没什么关系了。

ARCH(1)是对ε的平方及其滞后一项(one lag of the squared residuals)做回归。如果系数(下图的a1)不为0,则说明ARCH(1)成立,存在异方差的现象。

ARCH不检验系数和1的关系,系数和1的关系是检验covariance stationary时需要考虑的内容。

据此选择B选项。


对于上述ARCH模型的讲解可参考基础班M5的如下视频:


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