Frequently Asked Questions

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+φr(t-1)+θε(t-1)+ε(t)

where,

  • 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)=C+φΔr(t-1)+θε(t-1)+ε(t)

where,

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

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