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The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, yt = β0 + β1yt - 1 + εt, and yt = β0 + β1yt - 1 + β2yt - 2 + εt, were applied on the time series to make revenue forecasts. The relevant parts of Excel regression outputs are given below.
Model AR(1):
Model AR(2):
When for AR(1), H0: β0 = 0 is tested against HA: β0 ≠ 0, the p-value of this t test shown the output as 0.9590. This could suggest that the model yt = β1yt-1 + εt might be an alternative to the AR(1) model yt = β0 + β1yt-1 + εt. Partial output for this simplified model is as follows:
Find the revenue forecast for 2012 through the use of yt = β1yt-1 + εt.
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