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_timesat.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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