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6023统计中等derivationmedium

Long-Run Volatility (Not Variance) from GARCH Parameters

题目

A GARCH(1,1) model ht=ω+αrt12+βht1h_t=\omega+\alpha r_{t-1}^2+\beta h_{t-1} has ω=0.04\omega=0.04, α=0.12\alpha=0.12, β=0.80\beta=0.80. Here hth_t is the conditional variance of daily returns. Report the long-run (unconditional) daily volatility hˉ\sqrt{\bar h} as a decimal.

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