סמינרים

Thomas Yee

תאריך: 
ב', 11/04/2016 - 15:30 עד 16:30

Speaker: Thomas W. Yee, Department of Statistics, University of Auckland, New Zealand

Title: Vector generalized linear and other associated models


Abstract
This talk will give an overview of a GLM-like unified statistical
framework and a software implementation of it in the form of
the R package VGAM. The framework comprises about half a dozen
classes of models for standard fixed-effects regression. At its
heart are vector generalized linear models (VGLMs). They are not
limited to one linear predictor or the exponential family, as with
GLMs. VGLMs are estimated by iteratively reweighted least squares
and Fisher scoring. Being purposely general, application areas
include univariate and multivariate distributions, categorical
data analysis, extreme value analysis, and time series. A second
class called vector generalized additive models (VGAMs) allows for
smoothing. Another variant is the reduced-rank VGLM (RR-VGLMs)
class for dimension-reduction, and its offspring row-column
interaction models (RCIMs). The negative binomial distribution
is used to illustrate the utility of these models. Two other
classes are quadratic RR-VGLMs which is for ordination in ecology,
and RR-VGAMs which are a data-driven version of QRR-VGLMs.

Reference: "Vector Generalized Linear and Additive Models:
With an Implementation in R", Yee, T. W. (2015), Springer: New York

Ashis SenGupta

תאריך: 
ב', 04/04/2016 - 15:30 עד 16:30

מיקום: 
4412 (חדר הסמינרים)

Speaker:  Professor Ashis SenGupta, Indian Statistical Institute

Title: Dırectıonal Statıstıcs ın Hıgh Volatılıty Fınancıal Modelıng


Abstract

The term volatility refers to the variability of financial returns, which may change from time to time. In the modeling and forecasting of returns, e.g. from stock indices, stock prices and exchange rates, volatility is used at various points of the analysis. Due to the initiation of the open market and the emergence of international players in our domestic financial horizon, these returns have been experiencing high volatility previously not encountered. This has necessitated early detection of change-point in price distributions. Online optimal decision rules are presented for such early detection as using distributions in the exponential family. It is proven that a well designed multivariate portfolio consisting of suitably correlated profiles can achieve this detection at an earlier stage compared to univariate decision rules applied independently. This important feature is shown to persist even for portfolios with high coefficient of variation. However, the test is not robust against the popular volatility models such as the family of stable distributions. In general these families do not possess any analytical closed form for their probability density functions. This leads to the complexity of inference involving the parameters of such distributions. We overcome this problem by appealing to the area of probability distributions for directional data. First, methods of construction of probability distributions for such data are presented. This is a challenging problem leading to that of deriving distributions on smooth manifolds, such as those on the torus and the hypertorus. Then, it is shown how elegant methods for directional data can be exploited to derive crucial inference procedures for high volatility distributions. As an example, universal CAN estimators of the index (shape / characteristic exponent) parameter of some families of bivariate high volatility distributions are presented. The use of DDSTAP, a statistical package for directional data, developed by the speaker is also demonstrated for detection of change-point retrospectively. Once the change-point is detected, the estimation of Value at Risk, VaR, is of substantial importance. We briefly discuss this aspect also in the framework of high volatility models. The above methods are exemplified through several real-life financial data sets. Finally, several interesting and important problems for future research in this context are exposed.

עוד

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