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AR(p) parameters estimation

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Mario
Mario 2014-2-20
编辑： Shashank Prasanna 2014-2-28
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

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Shashank Prasanna
Shashank Prasanna 2014-2-20
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
  2 个评论
Mario
Mario 2014-2-28
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
Shashank Prasanna 2014-2-28
编辑：Shashank Prasanna 2014-2-28
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

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