Optimal heavy tail estimation – Part 1: Order selection

Supplement of Optimal heavy tail estimation – Part 1 : Order selection

Estimation of parameters in heavy - tailed distribution when its second order tail parameter is known ∗ †

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ-estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for b...

Heavy Tail Behavior and Parameters Estimation of GARCH (1, 1) Process

In practice, Financial Time Series have serious volatility cluster, that is large volatility tend to be concentrated in a certain period of time, and small volatility tend to be concentrated in another period of time. While GARCH models can well describe the dynamic changes of the volatility of financial time series, and capture the cluster and heteroscedasticity phenomena. At the beginning of ...

Order Estimation and Model Selection

Supplemental Material for ”Heavy Tail Robust Frequency Domain Estimation”

This appendix presents the theory for minimum mean-squared-error selection of the trimming fractile kT,h in the special case where ytyt−h has a symmetric distribution for h 6= 0 (Section B). It also contains details on the robust Whittle estimator (Section C), the omitted proofs of Theorems 2.3 and 3.3 (Section D), and omitted tables (Section E). Let γ̃T,h be the quantity used in practice for ce...