Applied Econometrics

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GARCH and ARCH - Summary ● ARCH – Autoregressive conditional heteroscedasticity: variance depends on past variance ● GARCH – generalized autoreg. cond. het.: variance is a weighted average of long-run variance (ω), the last period forecasted var. for this period (σ) and variance implied by most recent square residual (ε). ● Formally: ● ARCH(q): σ 2 = E(u t ) 2 = ω + α 1 (ε t - 1 ) 2 + …+ α q (ε t - q ) 2 ● GARCH(p,q): σ 2 = ω+α 1 (ε t - 1 ) 2 +…+α q (ε t - q ) 2 + β 1 σ 2 t – 1 + … + β p σ2 t - p.
GARCH - Motivation again... ● ACFand PACF of log returns (logs of first differences) – almost none significant (very common for financial time series) => ARIMA useless ● Conclusion: price development not predictable.
Page 1 and 2: Applied Econometrics Seminar: ARIMA
Page 3 and 4: ARMA and ARIMA Models ● Just the
Page 5: ARIMA models in JMulti ● Data: PX
Page 8 and 9: Comments to the results ● Still s
Page 12 and 13: ● But: Squares of log returns - v
Page 14 and 15: ● Plots for residuals of CEZ ARIM

Applied Econometrics

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