The only difference between ARIMA and ARIMAX is the **addition of an exogenous (external) variable**. The ARIMA model works on a single time series data (univariate) whereas ARIMAX uses multiple variables to include the external feature.

### Equation of ARIMAX

Δr(t)= c + φΔr(t-1) +θε(t-1) + ε(t) +β x

where,

**Δ****r(t)= r(t)-r(t-1) ,**difference in consecutive period.**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.**β =**coefficient for the external variable.**x**= value of the external variable.

### Equation of ARIMA

The equation of the ARIMA model is the same as ARIMAX except the external factor.

Δr(t)= c + φΔr(t-1) +θε(t-1) + ε(t)