Time series forecasting using particle filter I have searched high and low for a practical example of using a particle filter to assist with short term price forecasting using the local trend of a time series.
Could someone please share how a particle filter could be applied to time series using MATLAB.
I greatly appreciate any help on this.
 A: The primary idea behind a Kalman Filter is the optimal or nearly-optimal integration of an analytic model (and its errors) with real world measurements (and the associated measurement errors) to get a best estimate of both the most likely state and the uncertainty in this estimate.
I like to think of the following cartoon as a good way to describe this:

If you can provide the state update relationship then it is pretty straightforward to implement the Kalman filter.  The "particle" or "unscented" are about handling the state estimate uncertainty.  Given an initial state estimate $ \hat x_{n}(+)$ at time $ t(n)$ what is the function that produces the prediction $ \hat x_{n+1}(-)$ for time $ t(n+1)$?  (using notation from pg number 190 on discrete-extended Kalman filters).  What is "f"?
Would you think that assuming the value of the stock is constant over time is sufficient?  Linear?  Personally I like a system of four coupled 4th order ODE's.  They have given me some good numeric results.
