Innovation Approach
to
the Identification of Causal Models
in
Time Series Analysis
What causes the
time-dependency
in
geophysical time series?
Dynamical System & Time Series Model
ExpAR Models
&
non-Gaussian distributions
Causal Models
in
discrete time and continuous time
Time
discretizations
of
dx=f(x)dt+dw(t)
Application-(1)
Non-Gaussian time series
and
nonlinear dynamics
Same
Distribution
Different Dynamics
This implies
the
validity of innovation approach
When residuals of your
model
are non-Gaussian looking,
what would you do?
Application-(3)
RBF-AR & RBF Neural Net
Frost & Kailath(1971)’s theorem
Relations to Jazwinski(1970)’s scheme
Identification of the
chaotic Rikitake model
(Ozaki et at. 2000)
Innovation of the estimated model
Initial values & Estimated States
Example : Data
assimilation
in
meteorology
Mutual understanding : on the way
Hidden approximations
behind
perfect-model assumptions
Non-penalized L.S.
method(4D-VAR)
is even worse !
Prediction errors with assumptions
Innovation Ａｐｐｒｏａｃｈ to Ｓｐａｔｉａｌ ＴｉｍｅSeries:
Innovations in spatial dynamics
Space-Temporal Model with stimulus
Estimated Model tells you something