Reference no: EM132351207

For this assignment, use only the PROC AUTOREG code.

Question 1

Stock and Watson (2002) found that the standard deviation of real U.S. GDP growth during the 1984-2002 period was about 60 percent smaller than that during the 1960-1983 period. The GARCH framework is an ideal framework to test whether or not there was in fact a volatility break in 1984Q1 for the U.S. real GDP growth data.

Your task is to re-estimate this model and measure the extent of the volatility break in 1984Q1.

The following data series has been downloaded for the U.S. from the IFS database for the time period from 1959Q4 to 2002Q4. It is available in the file named gdp.

Gross Domestic Product, Real, Seasonally Adjusted Index

Now import this data series into SAS.

Write a SAS program that does all of the following:

a. Compute the growth rate in real GDP (as a percentage) and obtain a line plot for this data.

b. Is there formal evidence of time-varying heteroscedasticity in the U.S. real GDP growth rate data? Answer this question by estimating a pure AR(1) model for the U.S. growth rate data and then conduct the ARCH-LM test for this model. Remember to show the ARCH-LM test output and clearly explain your conclusion. For this question, use a 10 percent significance level.

c. Estimate an AR(1)-GARCH(1,1) model and show your estimation output.

d. Using the estimation model in part (c), obtain a line plot for the conditional volatility estimates for the U.S. real GDP growth rate data. Based on this graph, do you find evidence that the conditional volatility of the real GDP growth rate for the U.S. was in fact significantly lower starting in 1984Q1? Explain clearly. For clarity, you could draw a vertical line on your graph that indicates the first quarter of 1984.

Question 2

Recall the second SAS question from homework #3. You will now continue to work on the same question using the continuously compounded stock returns (in percentages) for the companies you selected and the S&P 500.

A quick reminder that, for this particular question, you were asked to use daily data for the adjusted closing stock prices from January 1, 2010 to June 30, 2019.

Write one SAS program that does all of the following:

a. Estimate an updated market model for your company given in equation (1) below and show the regression output.

R_t = α + β₁ R_m,t + β₂ R_comp,t + ε_t

Recall that, in this model, R is the stock return for an individual company (i.e. the company you selected) and Rm is the aggregate market return (i.e. S&P 500 return). Rcomp is the stock return for a competitor company in the same industry as the company you selected.
b. Is there formal evidence of time-varying heteroscedasticity in the company stock return? Answer this question by conducting the ARCH-LM test for the model shown in equation (1). Remember to show the ARCH-LM test output and clearly explain your conclusion.

c. Regardless of your answer to part (b) above, estimate an AR(1)-GARCH(1,1) model and show the estimation output. Don't forget to include the two explanatory variables that are already in equation (1) for this estimation and all remaining estimations.
Note: The conditional mean equation of the GARCH specification is not a pure AR process if you have additional X variables in equation (1).

d. Based on the estimation output, is there evidence of significant ARCH and GARCH effects in your company's stock returns? Explain briefly. Remember to use the relevant p-values when you answer this question.

e. Based on the estimation output, is your GARCH model stationary? Remember to conduct a relevant hypothesis test when you answer this question.

f. Is there evidence of a significant risk-return tradeoff for the company you selected? In order to answer this question, estimate an AR(1)-GARCH(1,1)-in-Mean model and show the estimation output. Then discuss your findings for the GARCH-in-mean coefficient.

g. Do you observe a significant leverage effect for the stock returns of your company? In order to answer this question, estimate an AR(1)-TGARCH(1,1) model and show the estimation output. Then discuss your findings for the leverage coefficient.

h. Using the information criteria, determine which one of the three models above fits the data the best. Using the optimal model, conduct a relevant hypothesis test to identify whether the company you selected can be considered as a neutral, aggressive, or defensive stock.

Attachment:- Quantitative Analysis in Equity Markets.rar