medium · FRM Part 1 Quantitative Analysis
A firm uses an AR(1) model for its inventory levels: x_t = 10 + 0.8 x_t-1 + ε_t.
What is the long-run mean of this process, and how quickly does it revert after a shock?
- Mean = 12.5; this process is deemed non-stationary overall.
- Mean = 10; reversion to that level occurs immediately next period.
- Mean = 80; the process behaves as a pure unit-root random walk here.
- Mean = 50; reversion speed is governed by the parameter 0.8.
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