Optimization algorithm: By default, Nelder-Mead is used in tseries::arma, while stats::arima employs the BFGS algorithm. Scale of the objective function: the objective function in tseries::arma returns the value of the conditional sums of squares, RSS stats::arima returns 0.5*log(RSS/(n-ncond)). Starting values of the coefficients: stats::arima sets the initial AR and MA coefficients to zero, while tseries::arma uses the procedure described in Hannan and Rissanen (1982) is employed to get initial values of the coefficients. There are three minor issues in tseries::arma compared to stats::arima that lead to a slightly different result in the ARMA model for the differenced series using tseries::arma and ARIMA in stats::arima.

Points 2 and 3 address different problems than mine, and even if I override the initialisation mentioned in point 1 by fit4<-arima(x,c(3,1,3),method='CSS',an=F,init=fit1$coe) Thanks for the hint for the fit1!Įdit2: I do not think this is a duplicate.

Sample code to demonstrate: library(tseries) I am interested in identifying where the difference comes from and with what parameters i can (if at all) fit the ARIMA to get the same coefficients of the fit as from the ARMA. The fitted parameters differ, which I attributed to the fitting method in ARIMA.Īlso, fitting an ARIMA(3,0,3) on the same data as ARMA(3,3) will not result in identical parameters, no matter the fitting method I use. In R (2.15.2) I fitted once an ARIMA(3,1,3) on a time series and once an ARMA(3,3) on the once differenced timeseries.

Arma 2 vs 3