Suppose that the monthly log returns, in percentages, of a stock follow the following Markov switching model:

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Suppose that the monthly log returns, in percentages, of a stock follow the following Markov switching model:

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where the transition probabilities are

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Suppose that , and s100 = 2 with probability 1.0.
What is the 1-step ahead volatility forecast at the forecast origin t = 100? Also, if the probability of s100 = 2 is reduced to 0.8, what is the 1-step ahead volatility forecast at the forecast origin t = 100?

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