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6025统计困难derivationmedium

Five-Step Forecast via the Mean-Reversion Formula

题目

For a GARCH(1,1) with ω=0.2\omega=0.2, α=0.1\alpha=0.1, β=0.8\beta=0.8, the one-step-ahead conditional variance is ht+1=3h_{t+1}=3. Using the closed form Et[ht+k]=hˉ+(α+β)k1(ht+1hˉ)E_t[h_{t+k}]=\bar h+(\alpha+\beta)^{\,k-1}(h_{t+1}-\bar h), compute the 5-step-ahead forecast Et[ht+5]E_t[h_{t+5}] as a decimal.

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