ARIMA is one of the most popular time series forecasting models and as its name indicates is made up of three terms:
AR: Stands for autoregression, which is nothing more than applying a linear regression algorithm using one observation and its own lagged observations as training data.
The AR model uses the following formula:
Where are the weights of the models learned from the previous observations and is the residual error for observation t.
We also call p the order of the autoregression model, which is defined as the number of lag observations included in the preceding formula.
For example:
AR(2) is defined as:
AR(1) is defined as:
I: Stands for integrated. For the ARIMA model to work, it is assumed that the time series is stationary or can be made stationary. A series is said to be stationary (https://en.wikipedia.org/wiki/Stationary_process) if its mean and variance doesn't change over time.