week 4 Flashcards
Define yt for stock price using GARCH
Properties of continuously compounded returns
Symmetric dist about mean for yt (drift)
Little autocorrelation in yt (hence ARMA inappropriate)
Strong autocorrelation in yt2
Variable volatility: local variance of process changes substantially across time
Formula for kurtosis
Calculate MGF for Gaussian RV
ARCH model
Crucially (G)ARCH models are defined by BOTH equations (which makes conversion to ARMA easier)
GARCH(p, q)
When to use EGARCH and why
When you suspect neg shocks may have diff effect size to pos shocks
When you don’t want to constrain params to no negativity (as log allows neg)
For modelling volatility
If you suspect volatility shocks have a large lasting impact, due to long memory of model
Express GARCH(1,1) as ARMA(1,1)
vt is a martingale difference (E = 0)
Estimation with GARCH and why
Significance of Kurtosis
In ARCH or GARCH models, if standardised residuals have high kurtosis it suggest that model may not be capturing dynamics of time series
Generally when to use ARCH and GARCH
When time series exhibits volatility clustering, periods of high volatility followed by low volatility
Finding γ or ρ for (G)ARCH models
Put into ARMA form as it is easier (?)
EGARCH in ARMA form
g(x) = ωx + λ(|x| - Eφ|x|)