ARMA: selection of lagged variables In the arma{tseries} documentation in R, they select a few lagged variables:
library(tseries)
data(nino)
arma(nino3.4, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL))

http://www.rdocumentation.org/packages/tseries/functions/arma
What do I call such a model? Can I call it an ARMA(19,0) even if some lagged values in-between are ignored?
 A: I would call it ARMA(19, 0). The AR and MA terms are typically identified by the maximum lag, even if some values in between are ignored. If you think about the way the ARMA(p, q) model is specified
$$x_t = \sum_{i = 1}^p\alpha_i x_{t-i} + \sum_{j=1}^q\beta_j w_{t-j} + w_t$$
you can imagine some $\alpha_i$ and $\beta_i$ values which happen to equal to zero.
A: This is AR(19) model, not ARMA. It has constraints on some lags, i.e. $\phi_2=0$, $\phi_4=0$ etc.
$$y_i=c+\sum_{k=1}^{19}\phi_k y_{i-k}+\varepsilon_i$$
Generally, it's better to not have these constraints without a good reason. They tend to create weird effects.
Often, like with R, AR(P) processes are estimated by the same routine as ARMA or even ARIMA. MATLAB is the extreme case where they're all estimated by `arima' function. That's why some people would call this ARIMA or ARMA process, but I like to emphasize that it is AR(P). It's quite different from integrated processes, in that it is stationary. It's also quite different from ARMA processes, e.g. it can be estimated by OLS while ARMA process would require something like MLE.
