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.christo...@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]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
