[R] Fitted values from AR model

[bogus christofer]

Thanks Eric.

Is it possible to know what R uses as the initial values? Are these
configurable?

On Fri, 12 Aug 2022 at 13:44, Eric Berger <ericjberger using gmail.com> wrote:

> The model that you are fitting to the data is an AR(2) model, which means
>
> y(t) = a0 + a1 * y(t-1) + a2 * y(t-2) + eps(t)                 (1)
>
> The fitting procedure estimates the coefficients a0, a1, a2 (and the
> variance of eps).
>
> After the coefficients have been estimated, the fitted values can be
> calculated using equation (1) (setting eps(t) = 0)
> using
> fitted(t) = a0 + a1 * y(t-1) + a2 * y(t-2)
>
> Assuming the series is given for t=1,2,...,20, there is no problem to
> apply equation (1) to get the
> fitted values for t=3,4,...,20. But there is a problem for t=1 and
> t=2. For example, for t=1, equation (1)
> says
>
> fitted(1) = a0 + a1 * y(0) + a2 * y(-1)
>
> But there are no values given for y(0) and y(-1). So, either no fitted
> values should be given for t=1,2, or some
> other method is being used. Apparently, the arima functions in R and
> python use different methodology
> to generate these two fitted points. (For all the other values, the
> fits are extremely close.)
>
> HTH,
> Eric
>
> On Thu, Aug 11, 2022 at 9:53 PM bogus christofer
> <bogus.christofer using gmail.com> wrote:
> >
> > Hi,
> >
> > I have below AR model and fitted values from the forecast package
> >
> > library(forecast)
> > dta = c(5.0, 11, 16, 23, 36, 58, 29, 20, 10, 8, 3, 0, 0, 2, 11, 27, 47,
> 63,
> > 60, 39)
> > fit <- arima(dta, order=c(2,0,0))
> > fitted(fit)
> >
> > This gives fitted values as
> >
> > Time Series:
> > Start = 1
> > End = 20
> > Frequency = 1
> >  [1] 13.461017  9.073427 18.022166 20.689420 26.352282 38.165635
> 57.502926
> > 9.812106 15.335303  8.298995 11.543320  6.606999  5.800820  7.502621
> > 9.930962 19.723966 34.045298 49.252447 57.333846 44.615067
> >
> >
> > However when I compare this result with Python, I see significant
> > difference particularly in the first few values as below
> >
> > from statsmodels.tsa.arima.model import ARIMA
> > dta = [5.0, 11, 16, 23, 36, 58, 29, 20, 10, 8, 3, 0, 0, 2, 11, 27, 47,
> 63,
> > 60, 39]
> > fit = ARIMA(dta, order=(2, 0, 0)).fit()
> > fit.predict()
> >
> > array([21.24816788, 8.66048306, 18.02197059, 20.68931006,
> > 26.35225759,38.16574655, 57.503278 , 9.81253693, 15.33539514,
> > 8.29894655,11.54316056, 6.60679489, 5.80055038, 7.50232004,
> > 9.93067155,19.72374025, 34.04524337, 49.25265365, 57.3343347 ,
> 44.6157026 ])
> >
> > Any idea why there are such difference between R and Python results will
> be
> > very helpful.
> >
> > Thanks,
> >
> >         [[alternative HTML version deleted]]
> >
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