Breakpoints and non linear regression
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 ! -- View this message in context: 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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