𝗙𝗔𝗔𝗡𝗚 𝗗𝗮𝘁𝗮 𝗦𝗰𝗶𝗲𝗻𝗰𝗲 𝗜𝗻𝘁𝗲𝗿𝘃𝗶𝗲𝘄 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻:
How does an ARIMA model work?

The most common question if you have a forecasting projects in your resume, or the role requires forecasting experience.

To explain this, let's start by breaking down ARIMA, and I mean literally -

AR - Auto-regressive component of model.
This assumes the future value depends LINEARLY on past values.

Typically, you use ACF/PACF plot to figure out how many of the past value (or 'p' value of ARIMA).

I - Integrated component of model.
It represents how to difference the values from themselves to make sure mean and variance is constant over time. Typically, you use a statistical test like ADF to figure out how much differencing you need (also called the 'd' value in ARIMA)

MA - Moving Average component of model.
This assumes future values depends LINEARLY on errors in forecasting made in prior time steps. Typically, you use ACF/PACF plot to determine past value (or 'q' values in ARIMA).

Note: You can also use packages like auto_arima in pmdarima in Python to do a grid search over a range of p,d,q parameter to fit your ARIMA model.

ARIMA essentially works by summing the differenced prior values and forecast errors. The reason why this simple formulation is ubiquitous, is because of its effectiveness and adaptability.

✅ It's able to account for stationary and non-stationary time-series.

✅ It can represent future values in terms of the few of the lagged previous values and forecast errors, making it interpretable and less likely to overfit.

✅ It can accommodate seasonality with its seasonal variation SARIMA, and exogenous variable i.e. features that might help predict future values of the time series apart from historical values of the same time series.

Credit- Karun

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