MPI fur Stromungsforschung and SFB 185 Nonlinear Dynamics.pdf

Divisiv e Strategies for Predicting Non
Autonomous
and Mixed Systems
K
P a w elzik
MPI f
ur Str
omungsforschung and SFB
Nonline ar Dynamics
Bunsenstr
D
G
ottingen
Germany
K
R
M
uller and J
en
GMD FIRST
German National R ese ar ch Center puter Scienc e
R udower Chausse e
D
Berlin
Germany
Key w ords
time series
prediction
nonstationarit y
divisiv e strategies
blind sep
aration
comp eting exp erts
Abstract
W e consider the problem of predicting time series originating from non
stationary and from mixed dynamical systems
It is sho wn that plexit y of
nding represen tations for the dynamics of suc h systems can b e drastically reduced if
p osite nature is tak en in to accoun t
Tw o paradigmatic cases are discussed
and their solutions presen ted
jump pro cesses and stationary mixtures
Examples
demonstrate that divisiv e approac hes can substan tially impro v e predictions of time
pared to metho ds that mo del the dynamics globally

In tro duction
Time series from real systems rarely originate from unique autonomous
dynamical systems
mon is the presence of additional noise
or nonstationarities
Also the fact that data often are sup erp ositions of
di
eren t sources c hallenges attempts to mo del the systems b pact
represen tations using
e
g
large s as in
In this con tribution
w e emphasize the imp ortance of iden tifying the
m ultiplicit y of the underlying dynamical subsystems to build adequate
mo dels for suc h data
Tw o paradigmatic situations are discussed
jump
pro cesses and stationary mixtures
Sudden c hanges of the dynamics constitute nonstationarities whic h
ur in man plex systems
Examples include m ultistable dynami
cal systems that are switc hed b y noise or con trol signals
non
autonomous
systems that are externally switc hed
as e
g
tec hnical systems
in whic h
failures ur
and also ecological and economical systems
plemen tary to jump pro