AR(p) parameters estimation

I have to fit the AR(p) model as:

 X_t = c + sum_{i=1}^p phi_i X_{t-i} + epsilon_t

 where p:order, phi:parameters to be estimated, c:constant, epsilon:white noise.

How can i estimate parameters' model?

I tried with ar function but i had only parameters phi. How can i estimate the constant term, c?

Any idea?

NB: I'm using ar function with Matlab2010

Thanks

Answer 1

[Shashank Prasanna]

If you have access to the Econometric Toolbox, you can estimate the model as shown in the first example:

http://www.mathworks.com/help/econ/arima.estimate.html

mdl = arima(2,0,0); % 2 the lag order
EstMdl = estimate(mdl,y); % y is your data

[Mario]

if I'm not wrong, the "estimate" method estimates parameters with loglikelihood optimization, I would need to use the OLS method.

Anyway, now I have to fit this model: Y_t=θ_0+θ_1*R_(t-1)+θ_2*R_(t-2)+θ_3*X_(t-1)+e_t

and I have to estimate parameters.

How can I do this?

Thanks in advance

[Shashank Prasanna]

I've answered a question similar to this before:

http://www.mathworks.com/matlabcentral/answers/62639-least-squares-estimation-code

In short, set up your lagged matrix and solve linear system X\y