# ARIMA, Time-Series Forecasting

We use ARIMA (Auto-Regressive Integrated Moving Average) to model time-series data for forecasting. ARIMA uses three basic concepts:

1. Auto-Regressive: The term itself points to regression, i.e., it predicts new value using regression over the previous lagged values of the same series. The lags used define its order
2. Integrated: This concept is used to remove trend (continuously increasing/decreasing time-series) from the time series. This is done by differencing consecutive values of time-series.
3. Moving Average: In this we perform regression by using the error terms at various lags. The lags used define its order

ARIMA works only on stationary data. If the input data is not stationary (detected via automated tests, i.e, different unit tests like famous Dickey-Fuller test), then stationary is achieved via differencing approach. The ARIMA forecasting equation for a stationary time-series is regression type equation in which predictors consist of previous response values at different lags. This also includes forecast errors at different lags.

$Predictor (y)\quad =\quad C\quad +\quad Weighted\quad sum\quad of\quad previous\quad y\quad and\quad previous\quad errors\quad at\quad various\quad lags$

Auto-regressive models and exponential smoothing are all special cases of ARIMA models

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