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where = 0.05911 and = 0.22296 from (8.60) and = 0.1314 and = 0.7187 from (8.61). The sample proportion of (in-sample) six-step-ahead forecasts that fell inside the 95 percent band was 99.9 percent with a standard error of approximately zero. The model was not tested out-of-sample after January 1997 so the stability of the parameters is not known. Overall, however, the GARCH(1, 1) does an excellent job of tracking the future variability of the S&P 500 index though the robustness should be tested out-of-sample to ensure stability of the estimated parameters. In general, the GARCH(1, 1) model performs better than ARCH(1) and OLS unconditional variance, especially for longer-term forecasts, due to its long-term memory. GARCH can also be used to compute the value at risk (VaR) of an asset or portfolio via historical or Monte Carlo simulation using GARCH to forecast the rolling volatility. VaR is computed by multiplying the computed (GARCH) volatility by the multiplication factor of the desired con dence level. For example, the 95 percent con dence multiplier is 1.645 and the 99 percent multiplier is 2.33. Figure 8.7, from Philip Best (1999), shows the price history of gold from November 12, 1991, to November 11, 1996. Best then computed the 95 percent VaR on a rolling basis (using a one-day horizon) based on a GARCH(1, 1) forecasted rolling volatility. The estimated GARCH(1, 1) equation was: 2 = 0.001865 + 0.4789 2 + 0.9457 2 t+1|t t t It was then compared to the actual percentage price changes the following day to determine how well the next-day percentage price changes could be captured inside the 95 percent VaR con dence bands using GARCH(1, 1) volatility estimates.
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Solving (5.24) for the ui, j (once we nd the intermediate qi, j ) is achieved through backward substitution. We can read ui+1, M directly (it is the value of the boundary), and if we solve in increasing i-incidental order we can nd all of the ui, j in the same manner: ui +1, M = qi , M y M ui +1, j = qi , j + pd ui +1, j +1 yj j = M + 1, . . . , M 1 (5.26)
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At the Devil-Linux System Configurator screen that is displayed, you see the menu options shown in Figure 9-5.
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wd is an object variable that exposes the Word Application object. wdDoc is an object variable that exposes the Word Document object. MyRange contains the range defining the contact list. MyCell is used to pass cell values into the string variables.
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Figure 11.5 Two short circuits. The wire in these circuits is bare wire. Where the wires are twisted together, the current would flow from one to the other. 137
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racemic calanolide A, cordatolide A, and inophyllum B were established, respectively, and enantioselective synthesis of optically active ( )-calanolide A and ( )inophyllum B were also accomplished. Some structural modi cations of ( )-calanolide A or ( )-calanolide B have been carried out. However, no compounds showed anti-HIV-1 activity superior to the two lead compounds (1 and 15). Hopefully, calanolide A continues to have promise as an anti-HIV drug in the near future.
had been worried that he might undergo a life change, reduce his stress, even retire. Retirement had never entered his mind, although he remembered a conversation with a night nurse who was giving him another dose of morphine a bit ahead of schedule because he couldn t sleep. She had asked if he wanted to make any changes in his life. A lot of people do, at times like this, she said as the morphine announced itself by tickles that spread across his face like bits of sand in a sudden wind. I think I like my life, Ben told her that night, I think I like things just the way they are. Then he added, except for this, pointing to his left shoulder. You re a lucky man, she said, rubbing his forehead with her soft hands. She had very soft hands. In that case, you should do something to celebrate your good fortune, because this surgery will keep you alive another 30 years. It was at the exact moment that they inserted the tiny camera into his vein and began the ascent to his heart, as he felt the warm blanket on his chest and the pinch of the intravenous tube taped to his left hand, as he heard the doctor say with no alarm, . . . and there it is . . . that Ben decided he was going to take some of his new salary and build a house in Danville, a house that was going to be exactly what his wife had wanted since they first married and moved into their Montclair home, the same home where their children were born, where they learned to drive, and where they said goodbye when they left for college. I m going to change the way I do business, and I m going to build a new house, Ben said to the doctor. The doctor laughed, mask moving out and in with the laughter, and then he said Let s fix this little problem first, and you can start on your personal transformation next week.
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