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A3. Let {r} denote the return series of a stock. We model returns by rt = μ + at where is a constant and {at} is the aut
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A3. Let {r} denote the return series of a stock. We model returns by rt = μ + at where is a constant and {at} is the aut
A3. Let {r} denote the return series of a stock. We model returns by rt = μ + at where is a constant and {at} is the autoregressive conditional heteroscedastic model, denoted by ARCH(m), where m is the order of the model. (a) Define the ARCH(2) model for {at} with parameters {ao, a₁, a2}. [3] (b) Given that the unconditional mean E(at) € 0, find the unconditional variance var (at) for a stationary ARCH (2) model in terms of its parameters {ao, a₁, a2}. [4] (c) Use the expression of the unconditional variance to state an additional condition a stationary ARCH (2) model must satisfy. [2] (d) Mention two characteristics of the data you should check before trying to fit an ARCH(m) model. [2] (e) Assuming the conditions in (d) are satisfied, how would you then determine if an ARCH (2) model is the most appropriate order? [1]
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