The annual sales for a company follow the AR(2) model X, 5+1.1.X-1-0.5.X-2+ with a = 2. = (a) If sales for 2012, 2011, 2010 were 10 units, 11 units, and 9 units, respectively, forecast sales for 2013 and 2014

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The annual sales for a company follow the AR(2) model X, = 5+1.1X-1-0.5.X-2+ with o² = 2.
(a) If sales for 2012, 2011, 2010 were 10 units, 11 units, and 9 units, respectively, forecast sales
for 2013 and 2014.
Also, calculate the variance of the errors in these forecasts, and 95% prediction intervals.
(b) Suppose the 2013 sales turn out to be 12 units. Calculate the updated forecast for 2014 and
compare it (and the variance of the error in the forecast) to the forecast value in part (a) above.
Transcribed Image Text:The annual sales for a company follow the AR(2) model X, = 5+1.1X-1-0.5.X-2+ with o² = 2. (a) If sales for 2012, 2011, 2010 were 10 units, 11 units, and 9 units, respectively, forecast sales for 2013 and 2014. Also, calculate the variance of the errors in these forecasts, and 95% prediction intervals. (b) Suppose the 2013 sales turn out to be 12 units. Calculate the updated forecast for 2014 and compare it (and the variance of the error in the forecast) to the forecast value in part (a) above.
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