- ARMA model has two components AR Auto Regressive and MA Moving Average. ARIMA model has an additional component Integration.
- ARMA models work well on stationary data whereas the ARIMA model works well on non-stationary data.
- The integration component in the ARIMA model converts the non-stationary data into stationary data.
- Integration is the number of times needed to difference a series in order to achieve stationarity.
- ARMA model takes two parameters p and q. ARMA(p,q) where p is the no of lags in the AR model and q is the no of lags in the MA model.
- ARIMA model takes three parameters p,d and q. ARMA(p,d,q) where d is no of differencing required to convert non-stationary data into stationary.
- ARMA(p,q) ~ ARIMA(p,0,q).
The below equations represent how the current value can be predicted using the past values.
1. ARMA Model Equation
- r(t),r(t-1) = current value and value one period ago.
- ε(t),ε(t-1) = current error term and one period ago.
- c = baseline constant factor.
- φ = value coefficient, what part of the last period value is relevant in explaining the current value.
- θ = error coefficient, what part of the last period value is relevant in explaining the current error value.
2. ARIMA Model Equation
- Δr(t)= r(t)-r(t-1) , difference in consecutive period.
- other is same as the ARMA model.