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Flashcards in Part 2 Deck (13):

News impact curve

- relates past return shocks to current volatility

- measures how new information is incorporated into volatility estimates

- symmetric for GARCH. However, empirical evidence: negative shocks have larger impact


Probability integral transform ut=G(zt)

- cdf has to be uniformly distributed and iid: ut ~ iid U(0,1)


Sandwich estimator in QML estimation

- QML estimation provides "robust" standard errors

- that gives asymptotically valid confidence intervals for the estimators (sandwich estimator)

- obtained as the square root of the diagonal elements of the matrix: omeg = A0^-1*B0*A0^-1 where A0: Hessian matrix and B0: outer product of the gradients


Problem in test of constant correlation?

- we know from cond corr that we should expect different corr depending on the vol

- therefore, a change in corr doesn't necessarily mean that corr indeed changed


Why test the adequacy of a non-normal distr in ML estimation?

- Consistency of QMLE is not guaranteed if incorrect distr used to maximize the likelihood

- Consistent only if either: (1) conditional mean is identically 0; (2) assumed and true error pdfs are symmetric about 0

- If not consistent, the reason is that it fails to capture the effect of the asymmetry distr on the conditional mean


Hill's estimator of the tail index

- Hill's estimator is the MLE of xi for tails drawn from a Pareto distr

- Only for Fréchet distr



- based on the inverse of the assumed cdf

Case of the gev:
- let (y1,...,ytau) be the standardized maxima over N-histories

- and y(1)<=...<=y(tau) the ordered maxima

- plot y(t) to Hxi^-1(t/tau)


Main difficulties of Hill's estimator of tail index

- it depends on the choice of the proportion of the sample used for computing the statistics

- If threshold too much in the tail -> innacurate estimates

- If too many obs -> tail obs are contaminated by obs from the central part


How generate non-linear dependence in multivariate t distr?

- by using normal mixtures

- idea is to introduce randomness into the cov matrix (via a positive mixing var W)


Excess distr fn in EVT?

- Fu(X) = Pr(Xt-u<=x ! Xt>u)

- measures the prob that the excess realization relative to the threshold (Xt-u) is below a certain value, given that u is exceeded


How adapt EVT if time-dependent returns?

- estimate the tail of the cond distr (rather than uncond)

- 2-step strategy:
(1) Fit a cond mean and vol model -> gives approx iid standardized residuals;

(2) Use EVT techniques to model the tail distr


Extrema or tail approach?

- tail approach: requires whole sample iid

- extrema approach: requires subsamples iid

- check for iidness of returns


Why DCC so successful?

2 main advantages over first gen models:

- DCC explicitly describes the corr matrix

- cond vars and corrs can be estimated separately (2-step estimation)