ARIMA (AutoRegressive Integrated Moving Average) is a widely used time series forecasting method that combines autoregression, differencing, and moving averages. ARIMA models are used to analyze and forecast time series data, making them valuable in various fields such as finance, economics, and epidemiology. Here’s an overview of ARIMA, its components, and how it works:
I. Components of ARIMA:
1. AutoRegressive (AR) Component:
- The autoregressive component refers to the correlation between a present observation and its past observations. The “p” parameter denotes the number of lag observations included in the model.
- The formula for the AR component is:
AR(p):Yt=ϕ1Yt−1+ϕ2Yt−2+…+ϕpYt−p+ϵt
2. Integrated (I) Component:
- The integrated component involves differencing the time series data to make it stationary. The differencing parameter, denoted by “d,” represents the number of times the series needs to be differenced to achieve stationarity.
- The formula for the differencing component is:
I(d):Yt′=Yt−Yt−d
