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MaPhySto Danish National Research Foundation Network in Mathematical Physics and Stochastics Funded by The Danish National Research Foundation |
The Concentrated Advanced Course and the Workshop will be given at the Institute of Mathematical Sciences, University of Copenhagen, HC Ørsted Institute. See the Infomation below how to get to the Institute. There will be 6 hours of lectures per day, 4 given by Richard A. Davis.
Generous financial support for Richard A. Davis by the Villum Kann Rasmussen Foundation is greatfully acknowledged.
The course is jointly organized by MaPhySto and the Graduate School of Mathematics and its Applications at the Institute of Mathematical Sciences.
The course is organized by Søren Asmussen (University of Aarhus), Henrik Hult (University of Copenhagen), Thomas Mikosch (University of Copenhagen), and Michael Sørensen (University of Copenhagen)
In this course, nonlinear time series models will be developed to model a wide-range of phenomena. These include generalized state space models for modeling time series of counts, GARCH and stochastic volatility models for modeling financial data, and continuous-time models that incorporate long memory. There will also be a discussion on fitting models with structural breaks.
The lectures will be complemented with practical hands-on experience in modeling data sets provided by the presenters.
a) Why nonlinear models?
b) Classification of white noise
e) Different types of white noise
f) Tests of white noise
g) Reversibility
h) All-pass models
a) GARCH models
i) basic properties
ii) estimation
iii) extreme value theory
iv) properties of sample correlations
b) Stochastic volatility models
i) autocorrelation function
ii) extreme value theory
iii) estimation
a) Parameter-driven models
b) Observation-driven models
c) Background on linear state-space models
d) Kalman filtering
e) Estimation for parameter-driven models
i) importance sampling
ii) approximate likelihood estimation
f) Estimation for GLARMA models
a) Minimum description length
b) Genetic algorithm
The Concentrated Advanced Course aims at the graduate student
in probability theory, statistics, finance, economics, insurance mathematics
and the researcher who wants to get an overview of methods
and techniques on modeling time series, as well as at the researcher
and the
practitioner who intend to apply non-linear time series models.
The course will be accessible
for Masters students with a background in statistics, econometrics
or time series analysis.
Alexander Lindner
GARCH processes - probabilistic properties
The focus of these lectures will be on financial
time series models, in particular on
the GARCH family and their probabilistic
properties. We will discuss
As continuous-time counterparts of the
(discrete-time) GARCH processes we present GARCH
diffusion limits and the COGARCH process, the latter
being a GARCH type process driven by a Levy process.
Here do you find the transparencies of
the 1st and
2nd Lecture .
Philippe Soulier
Modelling and estimating long memory in non linear time series
Slides in pdf
Gaussian and linear long memory processes have been quite exhaustively studied
in the past twenty five years, and a full statistical theory is available for
them but most applications require non-Gaussian, non-linear models. In the
first lecture, after giving a working definition of long memory, we will
present several classes of non-linear long memory processes and review their
main probabilistic properties. The second lecture will address the issue of
estimating long memory.
Peter Brockwell
Continuous-time ARMA processes
We will discuss
Catalin Starica
1. Is GARCH as good a model as the Nobel prize accolades would imply?
We investigate the relevance of the stationary, non-linear, conditional,
parametric modeling paradigm embodied by the Garch(1,1) process to
describing and forecasting the dynamics of returns of the Standard &
Poors 500 (S&P 500) stock market index.
A detailed analysis of the series of S&P returns featured in the
illustration of the use of the Garch(1,1) model in estimating and
forecasting volatility given in Section 3.2 of the Advanced Information
note on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred
Nobel reveals that the Garch(1,1) model severely over-estimated the
unconditional variance of returns during the period under study.
We test and reject the hypothesis that a Garch(1,1) process is the true
data generating process of the longer sample of returns on the S&P 500
stock market index between March 4, 1957 and October 9, 2003. We
investigate then the alternative use of the Garch(1,1) process as a local,
stationary approximation of the data and find that the Garch(1,1) model
fails during significantly long periods to provide a good local
description to the time series of returns on the S&P 500 and Dow Jones
Industrial Average indexes.
Catalin Starica
2. When did the 2001 recession
We develop a non-parametric, non-stationary framework for business-cycle
dating
based on an innovative statistical methodology known as Adaptive Weights
Smoothing (AWS). The methodology is used both for the study of the individual
macroeconomic time
series relevant to the dating of the business cycle as well as for the
estimation of
their joint dynamic.
We find evidence of a change in the methodology of the NBER's
Business-Cycle Dating Committee: an extended set of five monthly
macroeconomic indicators replaced in the dating of the last recession the
set of indicators emphasized by the NBER's Business-Cycle Dating Committee
in recent decades. This change seems to seriously affect the continuity in
the outcome of the dating of business cycle.
We find that, independent of the set of coincident indicators monitored,
the last economic contraction began in November 2000, four months before
the date of the NBER's Business-Cycle Dating Committee.
Other speakers will be announced later.
Talks are only by invitation.
Among others,
the speakers will cover the following topics:
Abstracts
There will be a regular
registration fee of 500 DKK (for Danes) or 70 Euros (for
non-Danes) for all participants of the Course.
The fee covers lunches from Monday to Friday,
coffee and cake during the coffee breaks.
Participation in the Workshop is free. It is possible to
order lunch on Friday, 1 October, 2004, for a fee of
100 DKK (for Danes) or 15 Euros (for non-Danes). If you do not need lunch, please register anyway.
The
participants are expected to have their expenses covered by their
home institutions or from other sources.
We intend to have an excursion to some sights in the neighborhood of
Copenhagen on Wednesday afternoon,
followed by a dinner in the
center of Copenhagen. We intend to have a bus excursion to
North Sealand, the island on which Copenhagen is located. Among
others,
we will visit Louisiana, the world famous museum of modern arts, located
in a charming park close to the sea.
There will be extra charges for the excursion
and the dinner to be paid on arrival at the conference site.
Please register via the registration form
at your earliest convenience but before August 31, 2004.
The programmes of the Course and the Workshop
will be on the web after September 1, 2004.
The course will start on Monday, 9:15, and stop on Thursday, 16:30.
Similar times apply to the workshop on Friday: 9:00-17:00.
We have a
page with information
on how to get to the HC Ørsted Institute, where the Course
will be given. Here is a
map
with the HC Ørsted Institute.
Do not hesitate to contact
the local organizers
Abstracts of the lectures
will frequently be updated
Programme of the Course
The Course is followed by a One-Day Workshop on
Non-Linear Time Series Modeling
The lecturers of the MaPhySto Course and some other invited speakers
will present results on their
most recent research on modeling with non-linear time series.
Programme of the Workshop
Registration
More Information
(hult@math.ku.dk)
for more information.