Business

Business

The file data3b.xls contains the daily stock price (Pt) of Toys Inc. from January 3, 2000 to
January 31, 2012. The total number of observations is 3152. Use data3b.xls and do the
following questions:
i) Generate a new variable, the daily stock returns volatility of Toys Inc.,
Rt = 100 × log(Rt/Rt‐1). Report the descriptive statistics (No of obs, Mean, SD, Min,
Max) and histogram for both variables, Pt and Rt. Explain the Jarque‐Berra test result.
ii) Draw line plots for the time series Pt and Rt separately.
iii) Using the ARCH LM test, test for the presence of conditional heteroskedasticity in
the return, Rt. (Choose 4 lagged squared residuals for the test.) Clearly write the
ARCH model and the null and alternative hypotheses, and discuss the test result.
iv) Estimate the GARCH(1,1) model for the return volatility of Toys Inc., and plot the
conditional variance estimates. Discuss the estimation result.
v) Estimate the Threshold GARCH(1,1) model. Test if there is any evidence of
asymmetric volatility or leverage effect. Clearly write the TGARCH model and the null
and alternative hypotheses, and discuss the test result.
vi) Test for the presence of return‐risk relationship using GARCH(1,1)‐M model.
Estimate all three forms of volatility in the return equation, i.e. the conditional
standard deviation, the conditional variance or the log of the conditional variance.
What do you conclude? Does the time varying premium exist?

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