Question

What are the model assumptions of the ARIMA (2,2,3) model?

Answer 1

ARIMA (Autoregressive integrated moving average):-
ARIMA modeling (sometimes called Box-Jenkins modeling), is an approach to modeling ARIMA processes—mathematical models used for forecasting. The approach uses previous time series data plus an error to forecast future values. More specifically, it combines a general autoregressive model AR(p) and general moving average model MA(q):
AR(p)— uses previous values of the dependent variable to make predictions.
MA(q)—uses the series mean and previous errors to make predictions.
ARIMA models are, in theory, the most general class of models for forecasting a time series which can be made to be “stationary” by differencing , perhaps in conjunction with nonlinear transformations such as logging or deflating .

A nonseasonal ARIMA model is classified as an "ARIMA(p,d,q)" model, where,
p is the number of autoregressive terms,
d is the number of nonseasonal differences needed for stationarity, and
q is the number of lagged forecast errors in the prediction equation.
In our model ARIMA(2,2,3) , p=2,d=2 and q=3.
The forecasting equation is constructed as follows. First, let y denote the dth difference of Y, which means, in our model
d=2: yt = (Yt - Yt-1) - (Yt-1 - Yt-2) = Yt - 2Yt-1 + Yt-2

ASSUMPTIONS :-
ARIMA models work on the assumption of stationarity (i.e. they must have a constant variance and mean). If your model is non-stationary, you’ll need to transform it before you can There are no known/suspected predictor variables
There are no level shifts.
There are no deterministic time trends of the form 1,2,3,...,t
There are no seasonal dummies
The model parameters are constant over time
The error process is homoscedastic .