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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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.