Applied Econometrics
Applied Econometrics
Applied Econometrics
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GARCH and ARCH - Summary<br />
● ARCH – Autoregressive conditional<br />
heteroscedasticity: variance depends on past<br />
variance<br />
● GARCH – generalized autoreg. cond. het.: variance<br />
is a weighted average of long-run variance (ω), the<br />
last period forecasted var. for this period (σ) and<br />
variance implied by most recent square residual (ε).<br />
● Formally:<br />
● ARCH(q): σ 2 = E(u t ) 2 = ω + α 1 (ε t - 1 ) 2 + …+ α q (ε t - q ) 2<br />
● GARCH(p,q):<br />
σ 2 = ω+α 1 (ε t - 1 ) 2 +…+α q (ε t - q ) 2 + β 1 σ 2<br />
t – 1 + … + β p σ2<br />
t - p.
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