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 r; = 1.14 + a;, a; = 0;€; 1 of = 0.119a-1 + 0.881o1+ -(4.276 – 0.08401), 1+ exp(-10a,-1) where all of the estimates are highly significant, the coefficient 10 in the exponent is fixed a priori to simplify the estimation, and {e;} are iid N(0, 1). Assume that a996 = -5.06 and o6 = 50.5. What is the 1-step-ahead volatility forecast ô996 (1)? Suppose instead that a996 = 5.06. What is the 1-step-ahead volatility forecast ô996(1)?

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Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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I need help with solution of this problem.Subject is Time Series and question is based on IGARCH.

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
r; = 1.14 + a,,
af = 0;E;
1
of = 0.119a-1 + 0.881o, +
(4.276 – 0.0840²1),
1+ exp(—10а,-1)
where all of the estimates are highly significant, the coefficient 10 in the
exponent is fixed a priori to simplify the estimation, and {;} are iid N (0, 1).
Assume that ag96 = -5.06 and o96 = 50.5. What is the 1-step-ahead volatility
forecast ô996 (1)? Suppose instead that ag96 = 5.06. What is the 1-step-ahead
volatility forecast og96(1)?
Transcribed Image Text: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 r; = 1.14 + a,, af = 0;E; 1 of = 0.119a-1 + 0.881o, + (4.276 – 0.0840²1), 1+ exp(—10а,-1) where all of the estimates are highly significant, the coefficient 10 in the exponent is fixed a priori to simplify the estimation, and {;} are iid N (0, 1). Assume that ag96 = -5.06 and o96 = 50.5. What is the 1-step-ahead volatility forecast ô996 (1)? Suppose instead that ag96 = 5.06. What is the 1-step-ahead volatility forecast og96(1)?
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