Motivated by the stylized facts on financial returns, the following ARCH(1) model has been introduced: rt...

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Motivated by the stylized facts on financial returns, the following ARCH(1) model has been introduced: rt = Otet, et~ iid N(0, 1) = w + air ²-1. لها (1) = This model successfully generates the stylized facts on financial returns; (i) mds (E [reFt-1] = 0), (ii) Volatility clustering, (iii) Heavier tail than normal distribution. (a) Show that the mds property E [rt|Ft-1] = 0 holds. (b) In ARCH(1) Model above, Var (re|Ft-1) = o² = w+ a₁1 (1) Derive the AR(1) represnetation in from this expression. (ii) It is known that the empirically estimated parameter value for a₁ is typically close to 1, say, 0.99. Discuss which stylized fact of financial return data is well captured by this result. (c) Show that the arch return in (1) has heavier tails than the standard normal distrib- ution, i.e. E [r] E [²]² Discuss why this result explains financial return distribution better than ud normal model. 23. Motivated by the stylized facts on financial returns, the following ARCH(1) model has been introduced: rt = Otet, et~ iid N(0, 1) = w + air ²-1. لها (1) = This model successfully generates the stylized facts on financial returns; (i) mds (E [reFt-1] = 0), (ii) Volatility clustering, (iii) Heavier tail than normal distribution. (a) Show that the mds property E [rt|Ft-1] = 0 holds. (b) In ARCH(1) Model above, Var (re|Ft-1) = o² = w+ a₁1 (1) Derive the AR(1) represnetation in from this expression. (ii) It is known that the empirically estimated parameter value for a₁ is typically close to 1, say, 0.99. Discuss which stylized fact of financial return data is well captured by this result. (c) Show that the arch return in (1) has heavier tails than the standard normal distrib- ution, i.e. E [r] E [²]² Discuss why this result explains financial return distribution better than ud normal model. 23.

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a To show that the meandifferencestationary MDS property holds for the ARCH1 model we need to demonstrate that the conditional expectation of the return at time t given the information set at time t1 ... View the full answer