Thread Subject: Stochastic process - parameter estimation

Hi,

I have a time series (sample) and suppose it consists of one or the sum of several stochastic processes, their structure already known (e.g. Brownian motion, Poisson process, ...). Now I'd like to estimate the respective (yet unknown) parameters so that in the end I'll have a best fit, regarding the characteristics of the sampled series.

Could anyone give me a hint how to proceed or where to begin? Is there a functionality implemented in MATLAB capable of doing this?

Thank you.

Thomas

Hi Thomas, depending on which toolboxes you have installed and which model you can reasonably posit for the process, there is a lot of functionality in place for that. Can you provide a bit more detail about your process. Can you reasonably assume that it is wide-sense stationary for example?

wayne

"Thomas " <meinl@iism.uni-karlsruhe.de> wrote in message <guu5u9$ajl$1@fred.mathworks.com>...
> Hi,
>
> I have a time series (sample) and suppose it consists of one or the sum of several stochastic processes, their structure already known (e.g. Brownian motion, Poisson process, ...). Now I'd like to estimate the respective (yet unknown) parameters so that in the end I'll have a best fit, regarding the characteristics of the sampled series.
>
> Could anyone give me a hint how to proceed or where to begin? Is there a functionality implemented in MATLAB capable of doing this?
>
> Thank you.
>
> Thomas

Hi Wayne,

As for the stationarity: I already cared about that, removing trends, seasonalities and so on, so that I may assume now that the remaining part can be considered purely stochastic ( in fact I'm trying to redo what I read in a paper, while I improved the step of removing seasonalities, and now want to follow the rest of their steps in order to compare the results).

The most basic form would be that the stochastic process X_t consists of

X_t = S_t + L_t

with L_t a long term stochastic process

dL_t = s_L dW_t^L

and S_t a short term Ornstein-Uhlenbeck process

dS_t = k(n-S_t)dt + s_S dW_t^S

(I hope the notation is comprehensible) with W_t^L and W_t^S two independent Brownian motions. Extended models also include Poisson processes.

Now I'd like to estimate s_L, s_S, k and n, give a sample (which is assumed to be stationary) of the time series.

Thanks a lot for your help.

Thomas

"Wayne King" <wmkingty@gmail.com> wrote in message <guu7f1$i7i$1@fred.mathworks.com>...
> Hi Thomas, depending on which toolboxes you have installed and which model you can reasonably posit for the process, there is a lot of functionality in place for that. Can you provide a bit more detail about your process. Can you reasonably assume that it is wide-sense stationary for example?
>
> wayne
>
> "Thomas " <meinl@iism.uni-karlsruhe.de> wrote in message <guu5u9$ajl$1@fred.mathworks.com>...
> > Hi,
> >
> > I have a time series (sample) and suppose it consists of one or the sum of several stochastic processes, their structure already known (e.g. Brownian motion, Poisson process, ...). Now I'd like to estimate the respective (yet unknown) parameters so that in the end I'll have a best fit, regarding the characteristics of the sampled series.
> >
> > Could anyone give me a hint how to proceed or where to begin? Is there a functionality implemented in MATLAB capable of doing this?
> >
> > Thank you.
> >
> > Thomas

Is there anyone who can give me a hint on this? Since I have a University's licence, I think I should have installed quite all toolboxes necessary.

Regards

Thomas

"Thomas " <meinl@iism.uni-karlsruhe.de> wrote in message <guu8me$7vk$1@fred.mathworks.com>...
> Hi Wayne,
>
> As for the stationarity: I already cared about that, removing trends, seasonalities and so on, so that I may assume now that the remaining part can be considered purely stochastic ( in fact I'm trying to redo what I read in a paper, while I improved the step of removing seasonalities, and now want to follow the rest of their steps in order to compare the results).
>
> The most basic form would be that the stochastic process X_t consists of
>
> X_t = S_t + L_t
>
> with L_t a long term stochastic process
>
> dL_t = s_L dW_t^L
>
> and S_t a short term Ornstein-Uhlenbeck process
>
> dS_t = k(n-S_t)dt + s_S dW_t^S
>
> (I hope the notation is comprehensible) with W_t^L and W_t^S two independent Brownian motions. Extended models also include Poisson processes.
>
> Now I'd like to estimate s_L, s_S, k and n, give a sample (which is assumed to be stationary) of the time series.
>
> Thanks a lot for your help.
>
> Thomas
>
> "Wayne King" <wmkingty@gmail.com> wrote in message <guu7f1$i7i$1@fred.mathworks.com>...
> > Hi Thomas, depending on which toolboxes you have installed and which model you can reasonably posit for the process, there is a lot of functionality in place for that. Can you provide a bit more detail about your process. Can you reasonably assume that it is wide-sense stationary for example?
> >
> > wayne
> >
> > "Thomas " <meinl@iism.uni-karlsruhe.de> wrote in message <guu5u9$ajl$1@fred.mathworks.com>...
> > > Hi,
> > >
> > > I have a time series (sample) and suppose it consists of one or the sum of several stochastic processes, their structure already known (e.g. Brownian motion, Poisson process, ...). Now I'd like to estimate the respective (yet unknown) parameters so that in the end I'll have a best fit, regarding the characteristics of the sampled series.
> > >
> > > Could anyone give me a hint how to proceed or where to begin? Is there a functionality implemented in MATLAB capable of doing this?
> > >
> > > Thank you.
> > >
> > > Thomas