# What is the Difference Between ARIMA and ARMA Model?

#### Components

• ARMA model has two components AR Auto Regressive and MA Moving Average. ARIMA model has an additional component Integration.

#### Input Data

• ARMA models work well on stationary data whereas the ARIMA model works well on non-stationary data.

#### Stationarity

• 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.

#### Parameters

• 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).

#### Equation

The below equations represent how the current value can be predicted using the past values.

#### 1. ARMA Model Equation

`r(t)=C+Ï†r(t-1)+Î¸Îµ(t-1)+Îµ(t)`

where,

• r(t),r(t-1) = current value and value one period ago.
• Îµ(t),Îµ(t-1) = current error term and one period ago.
• c = baseline constant factor.
• Ï† = value coefficient, what part of the last period value is relevant in explaining the current value.
• Î¸ = error coefficient, what part of the last period value is relevant in explaining the current error value.

#### 2. ARIMA Model Equation

`Î”r(t)=C+Ï†Î”r(t-1)+Î¸Îµ(t-1)+Îµ(t)`

where,

• Î”r(t)= r(t)-r(t-1) , difference in consecutive period.
• other is same as the ARMA model.