You work for Xanadu, a luxury resort in the tropics. The daily temperature in the region...

  

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You work for Xanadu, a luxury resort in the tropics. The daily temperature in the region is beautiful year-round, with a mean around 76 degrees Fahrenheit. Occasional pressure systems, however, can cause bursts of temperature volatility. Such volatility bursts generally don't last long enough to drive away guests, but the resort still loses revenue from fees on activities that are less popular when the weather isn't perfect. In the middle of such a period of high temperature volatility, your boss gets worried and asks you to make a forecast of volatility over the next 3 days. After some experimentation, you find that daily temperature yt follows Yt = μl + Et Et St-1 ~ N (0,0²), where o² = w+ a²²_1. Note that it is serially uncorrelated. Estimation of your model using historical daily temper- ature data yields = 76, = 1, and â = 0.4. Suppose that yesterday's temperature was 92 degrees. Answer the following questions. (a) Compute point forecasts for each of the next 3 days' temperature (that is, for today, tomorrow, and the day after tomorrow). (b) Compute point forecasts for each of the next 3 days' conditional variance. (c) Compute the 95% interval forecast for each of the next 3 days' temperature. (d) Your boss is impressed by your knowledge of forecasting and asks you whether your model can predict the next spell of bad weather. How would you answer his question? You work for Xanadu, a luxury resort in the tropics. The daily temperature in the region is beautiful year-round, with a mean around 76 degrees Fahrenheit. Occasional pressure systems, however, can cause bursts of temperature volatility. Such volatility bursts generally don't last long enough to drive away guests, but the resort still loses revenue from fees on activities that are less popular when the weather isn't perfect. In the middle of such a period of high temperature volatility, your boss gets worried and asks you to make a forecast of volatility over the next 3 days. After some experimentation, you find that daily temperature yt follows Yt = μl + Et Et St-1 ~ N (0,0²), where o² = w+ a²²_1. Note that it is serially uncorrelated. Estimation of your model using historical daily temper- ature data yields = 76, = 1, and â = 0.4. Suppose that yesterday's temperature was 92 degrees. Answer the following questions. (a) Compute point forecasts for each of the next 3 days' temperature (that is, for today, tomorrow, and the day after tomorrow). (b) Compute point forecasts for each of the next 3 days' conditional variance. (c) Compute the 95% interval forecast for each of the next 3 days' temperature. (d) Your boss is impressed by your knowledge of forecasting and asks you whether your model can predict the next spell of bad weather. How would you answer his question?

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