On Fri, 9 Nov 2012, Thomas Coquet wrote:
Hello,
I already tried and looked at the bfast package (very nice package by the
way!) as I am working on VI time series as well.
Good! :-)
However, my model is definitely not linear,
Not even after taking logs or some other transformation?
In principle, the breakpoint ideas can of course also be applied to
non-linear models but so far in my applications I could always find
transformations that lead rather naturally to roughly piecewise linear
relationships.
so in worst case scenario my idea was to use the bfast package to find
the breakpoints (with the harmonic fit) and then to fit the seasonal
part in each segment with my model (so basically almost what you are
suggesting - using harmonic to find breakpoints).
Yes, but for the log-transformed data...
But the breakpoints will not be dependent on my model, so this may be an
issue, isn't it ?
Yes.
The asymmetric gaussian fit has been recognized as being one of the best
fit for VI time series, and I used this method for periodic fit (so far
it was used only as a smoothing function of the time series, not as a
fit for the seasonal component).
The point would be to combine this method with an iterative breakpoint
method such as bfast to detect abrupt changes, but to do that I need to
find breakpoints in the seasonal trend with a non linear model (that is
the tricky part :) ).
In principle, you can set up the same type of procedure that bfast uses
with a non-linear model - as long as the objective function is additive in
the observations. But I wouldn't know of a (fast enough) fitting function
for such a segmented model in R.
hth,
Z
Thanks !
On Fri, Nov 9, 2012 at 2:00 PM, Achim Zeileis <achim.zeil...@uibk.ac.at>
wrote:
On Fri, 9 Nov 2012, thomas88 wrote:
Hello,
I have done some research about breakpoints (I am
not a statistician) and I
found out about the breakpoint, strucchange and
segmented packages in R
allowing to find breakpoints assuming linear model.
However, I would like to fit a periodic time series
with a non linear
(periodic) model, and I was wondering how I could
find breakpoints for this
model in R. Is it even possible ?
My model is an asymmetric gaussian fitting (cf
http://www.nateko.lu.se/personal/Lars.Eklundh/Institutionssida/IEEE_TGRS_ti
mesat.pdf)
with a linear-time-dependant amplitude (I am fitting
this model over the
whole time series).
*My ideas
*
1) I guess I am more interested in the breakpoints
of the "amplitude" of my
periodic function, so that I could assume a model of
the form:
Y ~ (a + b*t)*f(t), with |f(t)| <= 1, where f is a
periodic function to be
fitted to a non linear model, but where no
breakpoints should occur.
So basically, the breakpoints would only happen in
the (a,b) pair of
coefficients, which would be a linear regression.
However, as f is unknown,
this makes things harder and I don't have a lot of
extremas (min/max) to
detect breakpoints robustly...
2) To detect breakpoint with an harmonic model and
then to apply my non
linear regression on each segment.
I would probably first try whether the following leads to
reasonable fits
Y(t) = A * exp(b * t) * H(t)
i.e., a multiplicative model with an exponential trend and some
harmonic trend. By taking logs you then get
log Y(t) = log(A) + b * t + log(H(t))
->
log(Y(t)) = a + b * t + h(t)
so that you can fit a model with a linear trend plus harmonic
season to the log-series. And, of course, the harmonic trend can
then be built up up sin/cos at different frequencies and you
could fit the whole thing as a linear model to the log-series.
It's not quite the same model that you propose above but might
be an approach worth exploring. You could also look at the
"bfast" package which has a function bfastpp() for setting up
trend and harmonic season for a time series. And it also allows
for iterative fitting of separate trend and season breakpoints
in the time series.
hth,
Z
These two ideas could potentially work, however
these are workarounds.
Thank you for your advices !
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