Why can't ARIMA model large lags and/or long range dependence?
An ARIMA model with order of differencing d equal to 1 can model a time series with a unit root, which is a form of long-range dependence. If d=0 one has an ARMA model, which cannot model long-range dependence unless the number or AR or MA parameters is very high. To model long range dependence in a parsimonious manner, look at fractionally integrated ARMA models, known as ARFIMA models.