Questions / Quant research, Time-series reasoning
Variance and stationarity
A stationary zero-mean AR(1) has coefficient 0.5 and independent innovation variance 3. What is its unconditional variance?
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Answer: 4 units²
- Variance satisfies v = 0.5²v + 3, hence v=3/(1−0.25)=4.
Interview shortcut. AR(1) variance = σ²/(1 − φ²) = 3/0.75.
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