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Topic: Parameter estimation in ARIMA
Replies: 4   Last Post: Feb 16, 2013 10:48 AM

 Messages: [ Previous | Next ]
 Milos Milenkovic Posts: 189 Registered: 4/4/09
Re: Parameter estimation in ARIMA
Posted: Feb 15, 2013 4:20 AM

Dear Rick,
just once again to be sure. I have a time series. This data have trend and seasonal fluctuations, so I performed first difference and seasonal diff.
Now, on that adjusted data I determine the order of the model. After that, with obtained model order I have to estimate the coefficients of the model.
This process, according to the literature (not explicitly defined but what I can see) is done also (as the previous phase) on differenced data.
You say that the parameter estimation has to be done on original time series? So the differencing is only for model order determining.

Thanks once again!
Best,
M

"Rick " <rick.baker@mathworks.com> wrote in message <kfjaj6\$ng\$1@newscl01ah.mathworks.com>...
> "Milos Milenkovic" <m.milenkovic@mathworks.com> wrote in message <kfidh6\$esr\$1@newscl01ah.mathworks.com>...
> > Dear,
> > parameter estimation in ARIMA are performed on adjusted time series (first, seasonal differencing) or original nonstationary time series?
> > Best,
> > Milos

>
> Milos,
>
> If I understand you correctly, the parameters of an ARIMA model are estimated using the original, non-stationary series.
>
> To clarify, I mean that the data is not explicitly differenced to remove any seasonal and non-seasonal integration effects, and then that differenced data then fit to an ARMA model. For example, suppose you want to estimate an ARIMA(P,1,Q) model. We do not fit an ARMA(P,Q) model to the first difference of the original, non-stationary data.
>
> In other words, whatever differencing is required is performed by the underlying lag operator polynomials applied directly to the non-stationary data ? the lag operator polynomials do the work.
>
> HTH,
> -Rick

Date Subject Author
2/14/13 Milos Milenkovic
2/14/13 Rick
2/15/13 Milos Milenkovic
2/16/13 Rick
2/16/13 Milos Milenkovic