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.

However, my model is definitely not linear, 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).
But the breakpoints will not be dependent on my model, so this may be an
issue, isn't it ?

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 :) ).



Thanks !

On Fri, Nov 9, 2012 at 2:00 PM, Achim Zeileis <Achim.Zeileis@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_**timesat.pdf<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 !
>>
>>
>>
>> --
>> View this message in context: http://r.789695.n4.nabble.com/**
>> Breakpoints-and-non-linear-**regression-tp4649072.html<http://r.789695.n4.nabble.com/Breakpoints-and-non-linear-regression-tp4649072.html>
>> Sent from the R help mailing list archive at Nabble.com.
>>
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>>
>>

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