Reference no: EM132362864

Question 1

Diego models the monthly Mexican stock returns series (in percentages), Yt, as an AR(1) process and obtains the following results. The standard errors are given in parentheses.

Y^_t= 3.018 - 0.567 Y_t-1
       (2.184)  (0.039)

R² = 0.64; n = 200

a. What is the necessary condition for the Y_t series to be mean stationary? Conduct a suitable hypothesis test to determine whether this condition is met or not.

b. Suppose the true underlying data generating process for the stock returns series is in fact the AR(1) process shown on page 1. Compute the autocorrelation coefficients up to 6 lags, and then draw the plot of the AutoCorrelation Function (ACF) up to 6 lags.

Question 2

Paula models the daily Belgian stock returns series (in percentages), Y_t, as an MA(3) process and obtains the following estimation results. The standard errors are given in parentheses. You can safely assume that the underlying error process for the true model is in fact a white noise error process.

Y_t = 0.821 + 1.245 e_t-1 + 1.498 e_t-2 + 1.315e_t-3

      (0.389)   (0.333)      (0.507)       (0.770)

R² = 0.53; n = 120

a. What is the mean-reverting level for this data process?

b. Suppose the process is currently at μ. Then, in time period t a shock occurs to the system. In other words. For simplicity, assume that there are no other shocks prior to or after this shock. Write the relevant equations to trace the impact of this shock from period (t-1) to (t+4) and show that the impact of the shock leaves the system after a finite number of periods.

c. Using your work from part (b), draw a relevant graph to trace the impact of the shock to the system. In particular, show what happens from period (t-1) to (t+4) on your graph.

Question 3

The SAS regression output for an AR(2)-TGARCH(1,1)-in-Mean model is given below for the Chinese stock market return data. Answer the questions below using this SAS output.

‘Estimation results for the AR(2)-TGARCH(1,1)-Mean model'

The AUTOREG Procedure
Dependent Variable: chinaret

a. Is there evidence of a significant leverage effect for the Chinese stock market return data? Write down the relevant p-value and answer this question using the p-value method. If significant, then also discuss the coefficient estimate on the leverage effect variable.

b. Is there evidence of a significant risk-return tradeoff for the Chinese stock market return data? Write down the relevant p-value and answer this question using the p-value method. If significant, then also discuss the coefficient estimate on the risk-return variable.

c. Is the TGARCH-in-Mean model stationary? In order to answer this question, a relevant hypothesis test was conducted. The resulting SAS output with the test statistic and p-value are given on the next page. Based on this output, do you conclude that the model is stationary or not? Explain clearly.

Final Examination

Use the SAS software to answer the following question. Note that this question has two parts - Part A and Part B.

Remember to show both your SAS program and the relevant SAS output. There should be one complete SAS program.

Use a 5% significance level unless otherwise stated. Use only the p-value method to answer any hypothesis test questions.

Question

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.

You are given the following data series for the U.S. (from the IFS database) for the time period from 1959Q4 to 2002Q4:

Gross Domestic Product, Real, Seasonally Adjusted Index

Import the data series named ‘gdpdata' into SAS, and write a SAS program that does all of the following:

Part A

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

b. Estimate a pureARMA(1,2) model and show the estimation output.

c. Obtain the forecasted values forthe real GDP growth rate for the forecast horizon, which is the last four quarters of the sample. Thenplot in one graph the actual and the forecasted GDP growth (along with the 95% confidence interval for the forecasts) only for the forecast horizon.

d. Obtain the RMSE value for the ARMA(1,2) model forecasts, and comment on how well the forecasts resemble the actual data.

Part B

e. Is there formal evidence of time-varying heteroskedasticity 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.

f. Estimate an AR(1)-GARCH(1,1) model and show your estimation output. Are there significant ARCH and GARCH effects in the model?

g. Estimate an AR(1)-GARCH(1,1) - in - Mean model and show your estimation output.Is this model stationary? Conduct a suitable hypothesis test to answer this question.

h. Using the estimation model in part (f), 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 briefly.

Attachment:- Equity Analysis in Equity Markets.rar