Tid: 14 januari 2002 kl 1600-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Fredrik Strandberg.
Titel: Tails and outliers in financial time series. (Examensarbete)
For the covariance/variance estimation of financial instruments, a bank may want to exclude values that are very influential and seem "not to fit in". We consider how such aberrant observations, "outliers", can be defined, modelled and detected within univariate and multivariate frameworks of dependent and independent data.
The returns of financial instruments typically have heavier tails than the normal distribution, and we capture this property by using models with heavy tails or by extending the normal model with outliers. We use a GARCH model for the stochastic volatility, and pay extra attention to the often used GARCH(1,1) model, its benefits and drawbacks.
In the univariate time series case, we investigate how outliers can be modelled and detected in ARMA models and also adapt the method to GARCH(1,1) models. We show how the tails can be modelled with Extreme Value Theory, using the POT-method or the Hill estimator, and show an application that combines a GARCH model with the POT-method to improve the results. We also construct an empirically found well-working robust estimate of the standard deviation.
In the multivariate case, some definitions are generalized and a practical distance measure, the Mahalanobis distance, is used. We also show how the multivariate technique can be used on a univariate sample.
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