Suppose that the monthly log returns of GE stock, measured in percentages, follow a smooth threshold IGARCH
Question:
Suppose that the monthly log returns of GE stock, measured in percentages, follow a smooth threshold IGARCH \((1,1)\) model. For the sampling period from January 1926 to December 2008, the fitted model is
where all of the estimates are highly significant, the coefficient 10 in the exponent is fixed a priori to simplify the estimation, and \(\left\{\epsilon_{t}\right\}\) are iid \(N(0,1)\). Assume that \(a_{996}=-5.06\) and \(\sigma_{996}^{2}=50.5\). What is the 1-step-ahead volatility forecast \(\widehat{\sigma}_{996}(1)\) ? Suppose instead that \(a_{996}=5.06\). What is the 1 -step-ahead volatility forecast \(\widehat{\sigma}_{996}(1)\) ?
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