I think that you can use Box-Jenkins models

1.Non-seasonal autoregressive(AR) model of order 1

=\phi_1*z_{t-1}+a_t,where a_t is random error(or shock)~N(0,1)

2.Non-seasonal moving average (MA) model of order 1

z_t=a_t-\teta_1*a_{t-1}

Then after you have to differentiate once because our model are of order 1 to induce

stationarity in other case mathematically ODE models,

Consider an interval [a,b] such that y'(x)={y(x+h)-y(x)}/h

using forward scheme h*y'(x)=y_{i+1} - y_i, i>0

using backward scheme h*y'(x)=y_i - y_{i-1},i>0

with initial condition I mean y(a)=a given value and

y(b)=a given value different from

It means that you will get a matrix form and your solution will be a matrix(n,1)

through this ODE above you can express your z_t to fit the ARIMA model

Thanks. Most of the published algorithms are like a foreign language. Can you help me with an algorithm preferably in matlab or fortran. Thanks

Check if this paper can help you:

Parameter and state estimation of experimental chaotic systems using synchronization

John C. Quinn, Paul H. Bryant, Daniel R. Creveling, Sallee R. Klein, and Henry D. I. Abarbanel

Phys. Rev. E 80, 016201 – Published 6 July 2009

Thanks Cerdeira, i was able to get the publication. However, my time series are natural hence no corresponding dynamical systems. I tried the following which is quite common in literature

(i) obtain the dimension of the system

(ii) numerically differentiate the system

(iii) model with a set of equation as described in Palvov et al Tech. Phys. Lett. 23 (4), April 1997

However, i still have some issues

Try NumXel. it offers a simple program in Excell to do ARMA