Autoregressive-moving-average (ARMA): In the statistical analysis of time series, autoregressive-moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the auto-regression and the second for the moving average. Given a time series of data Xt, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The model consists of two parts, an autoregressive (AR) part and a moving average (MA) part. The model is usually then referred to as the ARMA(p,q) model where p is the order of the autoregressive part and q is the order of the moving average part . There are a number of modelling options to account for a non-constant variance, for example ARCH (and GARCH, and their many extensions) or stochastic volatility models.




An ARCH model extend ARMA models with an additional time series equation for the square error term. They tend to be pretty easy to estimate (the fGRACH R package for example).




SV models extend ARMA models with an additional time series equation (usually a AR(1)) for the log of the time-dependent variance. I have found these models are best estimated using Bayesian methods (OpenBUGS has worked well for me in the past). You can fit ARIMA model, but first you need to stabilize the variance by applying suitable transformation. You can also use Box-Cox transformation. This has been done in the book Time Series Analysis: With Applications in R, page 99, and then they use Box-Cox transformation. Check this link Box-Jenkins modelling Another reference is page 169, Introduction to Time Series and Forecasting, Brockwell and Davis, "Once the data have been transformed (e.g., by some combination of Box-Cox and differencing transformations or by removal of trend and seasonal components) to the point where the transformed series X_t can potentially be fitted by a zero-mean ARMA model, we are faced with the problem of selecting appropriate values for the orders p and q." Therefore, you need to stabilize the variance prior to fit the ARIMA model.