Visit below website to get your answer. commonly ARMA,ARIMA,ARMAX,SARIMA and so on used to analysis and forecast the time series and reveal the behavior of a specific dataset.
Hi, The AR(p) and MA(q) models (p and q are the orders of the models) you asked are (stationary) time series models, witch are subclass of ARMA(p,q), which are used (with some details!) to model the available auto-correlation structure in the time series data (like rainfall in a region measured in an interesting time scales for example monthly or yearly, etc).
To learn more, I recommend you google the keyword(s) of your interesting field+ ARMA and have a look on the following book (or similar ones).
Arma and Arima are just two models in the huge area of time series analysis, and basically methods of data fitting. There used to be a lot of debate about the merits of all these models, and that gave rise to various notions of causality like Granger causality. An expert in the field is Manfred Deistler, who wrote important books about time series analysis, about its mathematical structures, but also about its applicability . Highly recommended, just consult the website of publisher Springer Verlag.