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In estimating the regression in problem #2, you are also concerned that the t-statistics may be inflated because of the presence of conditional heteroscedasticity. There are 214 observations and 3 independent variables.

In estimating the regression in problem #2, you are also concerned that the t-statistics may be inflated because of the presence of conditional heteroscedasticity. There are 214 observations and 3 independent variables.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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  1. ) In estimating the regression in problem #2, you are also concerned that the t-statistics may be inflated because of the presence of conditional heteroscedasticity. There are 214 observations and 3 independent variables. 

    You conduct a regression of the squared residuals against the dummy variables X1, X2, and X3 and find that for the squared residuals regression:

 

Multiple R

0.4145

 

R Square

0.1718

 

Adjusted R Square

0.1600

 

SEE

92.3760

 

  1. Conduct a Breusch–Pagan test at the 0.05 level to see if conditional heteroskedasticity is present and from your results, what needs to be done?
2. You believe that the VIX trades in regimes where its average level is significantly different. You define four regimes from 2004 through 2021: June 2008 through October 2011 (financial crisis); February 2020 through March 2021 (the COVID-19 crisis); the 12-month transition periods before and after the financial crisis and the current transition period after the COVID-19 crisis; and the remaining periods of low volatility. In order to test your hypothesis, you examine month-end values of the VIX from January 2004 through October 2021 (214 observations) and conduct the following regression: Dependent variable Y: Month-end value of VIX Dummy variable X1: Financial Crisis: 1 if between June 2008 through Oct 2011, 0 if not COVID-19 crisis: 1 if between Feb 2020 through March 2021, 0 if not Transition period: 1 if in 12 months before or after the financial crisis or Dummy variable X2: Dummy variable X2: the current period since the COVID-19 crisis (June 2007 – May 2008, Nov 2011 – Oct 2012, or April 2021- Oct 2021) The results for the regression are as follows Coefficients Standard Error Intercept 14.63 0.5226 financial crisis 13.71 1.0610 COVID-19 crisis 15.71 1.6643 transition 5.40 1.1835 а. How would the introduction of Dummy variable X4: Low volatility period (Jan 2004 – May 2007, or Nov 2012 - Jan 2020) affect the output of this regression? Why? The introduction of dummy variable X4 will let us know how the vix varied after the financial crisis as compared to before the financial crisis. This will help us predict the yix after covid-19 b. Which of the coefficients are significant at the 0.01 level? T-value = Coefficients/Standard error Coefficients Standard Error Beta/Standard Error P-Value Intercept 14.63 0.5226 27.995 0.000 Financial Crisis 13.71 1.061 12.922 0.000 Covid-19 15.71 1.6643 9.439 0.000 Transition 5.4 1.1835 4.563 0.000 Because all the respective p-values are less than 0.01. All of them are significant at the 0.01 level. C. According to the regression result, what was the average value of the VIX during the COVID-19 Crisis? Vix = 14.63 + 13.71 *1+ 15.71 + 5.4 * 0 = 28.34
Transcribed Image Text:2. You believe that the VIX trades in regimes where its average level is significantly different. You define four regimes from 2004 through 2021: June 2008 through October 2011 (financial crisis); February 2020 through March 2021 (the COVID-19 crisis); the 12-month transition periods before and after the financial crisis and the current transition period after the COVID-19 crisis; and the remaining periods of low volatility. In order to test your hypothesis, you examine month-end values of the VIX from January 2004 through October 2021 (214 observations) and conduct the following regression: Dependent variable Y: Month-end value of VIX Dummy variable X1: Financial Crisis: 1 if between June 2008 through Oct 2011, 0 if not COVID-19 crisis: 1 if between Feb 2020 through March 2021, 0 if not Transition period: 1 if in 12 months before or after the financial crisis or Dummy variable X2: Dummy variable X2: the current period since the COVID-19 crisis (June 2007 – May 2008, Nov 2011 – Oct 2012, or April 2021- Oct 2021) The results for the regression are as follows Coefficients Standard Error Intercept 14.63 0.5226 financial crisis 13.71 1.0610 COVID-19 crisis 15.71 1.6643 transition 5.40 1.1835 а. How would the introduction of Dummy variable X4: Low volatility period (Jan 2004 – May 2007, or Nov 2012 - Jan 2020) affect the output of this regression? Why? The introduction of dummy variable X4 will let us know how the vix varied after the financial crisis as compared to before the financial crisis. This will help us predict the yix after covid-19 b. Which of the coefficients are significant at the 0.01 level? T-value = Coefficients/Standard error Coefficients Standard Error Beta/Standard Error P-Value Intercept 14.63 0.5226 27.995 0.000 Financial Crisis 13.71 1.061 12.922 0.000 Covid-19 15.71 1.6643 9.439 0.000 Transition 5.4 1.1835 4.563 0.000 Because all the respective p-values are less than 0.01. All of them are significant at the 0.01 level. C. According to the regression result, what was the average value of the VIX during the COVID-19 Crisis? Vix = 14.63 + 13.71 *1+ 15.71 + 5.4 * 0 = 28.34
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