# Time series (stochastic process) estimating parameters using characteristic function

I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector of unknown parameters. I need to esimate vector of unknown parameters $\theta$ of characteristic function.

I tried to find a PDF using the inverse Fourier transform to use the maximum likelihood method, but the characteristic function is too complicated for that. I also thought about building the empirical characteristic function using the time series of assets and to estimate parameters using the least square method, but I do not know how to build the empirical characteristic function, because time series is not just a sample of random variables, it is a random process that depends on time.

• Is this question about Mathematica the software, or a general mathematics question? – Mr.Wizard Dec 11 '13 at 19:51
• It is a general question, but I'm triyng to solve it using Mathematica. – Dmitry Pavliv Dec 11 '13 at 20:16
• Could you add a specific small example, possibly a simplified version of your actual problem ? – b.gates.you.know.what Dec 12 '13 at 10:02
• Also asked on math.se: math.stackexchange.com/questions/602898/… – Ben Dec 12 '13 at 10:48