Unlocking Time Series Secrets With ARIMA

A Comprehensive Guide to Understanding and Implementing ARIMA

Widely used for time series analysis, ARIMA models combine autoregression, differencing, and moving averages to make accurate observations based on historical data. This article demystifies the ARIMA model, providing you with essential insights, practical applications, and a step-by-step guide to mastering time series in Python.

The Foundations of ARIMA

ARIMA stands for autoregressive integrated moving average. It is a popular and widely used statistical model for analyzing and forecasting time series data. The ARIMA model combines three key components: autoregression (AR), differencing (I for integrated), and moving average (MA). In further details, it is as follows:

• The autoregressive part (AR) of the model specifies that the output variable depends linearly on its own previous values. It is denoted by p, which is the number of lag observations included in the model.
• The integrated part (I) of the model involves differencing the data series to make it stationary. Stationarity implies that the properties of the series do not depend on the time at which the series is observed. It is denoted by d, which is the number of times the raw observations are differenced.
• The moving average part (MA) specifies that the output variable depends linearly on the past error terms. It is denoted by q, which is the size of the moving average window.

Hence, the ARIMA model is simply a function of p, q, and d:

The three above parameters are determined in the data preparation step by using the autocorrelation function (ACF) and the partial autocorrelation function (PACF). How is this done? Well, first let’s define both functions:

• The autocorrelation function (ACF) measures the correlation between observations of a time series separated by different time lags. It helps in identifying the strength and direction of the relationship between the observations at different lags. A gradual decline in autocorrelations (i.e., “decay”) suggests non-stationarity in the series.

Significant spikes in the ACF plot indicate strong correlations at…