Explanation:
Given the AR(1) model: R&DSpend_{t+1} = 0.25 + 0.12(R&DSpend_t)
Current value: R&DSpend_t = $0.15
Step 1: One-quarter-ahead forecast
R&DSpend_{t+1} = 0.25 + 0.12(0.15) = 0.25 + 0.018 = $0.268
Step 2: Two-quarter-ahead forecast
R&DSpend_{t+2} = 0.25 + 0.12(R&DSpend_{t+1}) = 0.25 + 0.12(0.268) = 0.25 + 0.03216 = $0.28216
The two-quarter-ahead forecast is approximately $0.282, which corresponds to option B.
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An analyst forecasts the R&D spend of a pharmaceutical company using an AR(1) process by modeling the quarterly R&D spend per dollar of revenue. The estimated model is:
R&DSpend_{t+1} = 0.25 + 0.12(R&DSpend_t)
If the current quarter's R&D spend per dollar of revenue is $0.15, the two-quarter-ahead forecast of the R&D spend based on this model is closest to:
A
$0.268
B
$0.282
C
$0.490
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