Explain what Autoregressive Conditional Heteroskedastic (ARCH) effects are and why they are particularly likely to occur in financial data.

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Question 1.

(a) Explain what Autoregressive Conditional Heteroskedastic (ARCH) effects are and why they are particularly likely to occur in financial data.

[5 Marks] (b) Suppose you wish test for the presence of ARCH effects in a stock market index. Explain how you would conduct a test for the presence of the 4th order ARCH effects in an ARMA (1,1) model.

[8 Marks]

(c) Using monthly data for yt, the FTSE100 index, from January 1992 to December 2005, the following set of results were obtained:

ŷt = 0.75, (0.21)

ổ = 1.76 + 0.07 _ +0.240_1+0.87_1_1

(0.57) (0.02)

(0.12)

R2 = 0.46

(0.42)

=

Values in () are the standard errors of the coefficient estimates and It-1 = 1 ifut-1 < 0, It-1 = O otherwise. σt-1 is the conditional deviation.

i.

ii.

What role does the final term in the above conditional variance equation serve?

[4 Marks] What is the interpretation of the estimated value of lagged conditional variance (0-1), 0.24?

iii.

[4 Marks]

-1

=

With reference to conditional variance equation, if σ?-1 = 0.74, consider that ût-1 ±0.5. Estimate the value of of, for a positive shock (+0.5) and a negative shock (-0.5).

[4 Marks]

 

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