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小强爱英语 · 2023年06月09日

是否可以这么解?

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NO.PZ202208220100000302

问题如下:

You are a junior analyst at an asset management firm. Your supervisor asks you toanalyze the return drivers for one of the firm’s portfolios. She asks you to constructthree regression models of the portfolio’s monthly excess returns (RET),starting with the following factors: the market excess return (MRKT), a value factor(HML), and the monthly percentage change in a volatility index (VIX). Nextyou add a size factor (SMB), and finally you add a momentum factor (MOM).Your three models are as follows:


Your supervisor is concerned about conditional heteroskedasticity in Model 3 and asks you to perform the Breusch–Pagan (BP) test. At a 5% confidence level, the BP critical value is 11.07. You run the regression for the BP test; the results are shown in Exhibit 1.


Now the chief investment officer (CIO) joins the meeting and asks you to analyze two regression models (A and B) for the portfolio he manages. He gives you the test results for each of the models, shown in Exhibit 2.


The CIO also asks you to test a factor model for multicollinearity among its four explanatory variables. You calculate the variance inflation factor (VIF) for each of the four factors; the results are shown in Exhibit 3.



Identify the type of error and its impacts on regression Model A indicated by the data in Exhibit 2.

选项:

A.Serial correlation, invalid coefficient estimates, and deflated standard errors.

B.Heteroskedasticity, valid coefficient estimates, and deflated standard errors.

C.Serial correlation, valid coefficient estimates, and inflated standard errors.

解释:

A is correct. The Breusch–Godfrey (BG) test is for serial correlation, and for Model A, the BG test statistic exceeds the critical value. In the presence of serial correlation, if the independent variable is a lagged value of the dependent variable,then regression coefficient estimates are invalid and coefficients’ standard errors are deflated, so t-statistics are inflated.

类比为正向序列相关,系数bo bi不受影响,不受影响是否可以说是有invalid?

1 个答案

袁园_品职助教 · 2023年06月10日

嗨,努力学习的PZer你好:


invalid的意思是无效,说明这个系数估计是受影响的。

这里判断是根据这个条件来的。

我们在基础班讲义里面说过,当这个自变量是因变量的滞后项时(因变量是Yt,自变量中有Yt-1),这个系数估计是无效的。


注意:这里和下面的正向序列相关是两回事。正向序列相关是指残差项自己和自己相关,但自变量中没有因变量的滞后项,也就是红框里面的第一种情况,系数估计有效,但standard error无效;但是如果是自变量是因变量的滞后项这种情况,说明这个残差项是和因变量相关的,这个情况下系数估计也是无效的,standard error也无效。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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