An Autoregressive Integrated Moving Average (ARIMA) model is a statistical analysis model used in time series analysis to forecast future trends. It is a generalization of an Autoregressive Moving Average (ARMA) model, where both models are fitted to time series data to better comprehend the data or to forecast upcoming series points. ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance), where an initial differencing step (corresponding to the "integrated" part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.e., the trend) .

ARIMA models consist of three parameters: p, d, and q, which are non-negative integers. The p parameter is the order (number of time lags) of the autoregressive model, the d parameter is the degree of differencing (the number of times the data have had past values subtracted), and the q parameter is the order of the moving-average model. Non-seasonal ARIMA models are generally denoted ARIMA(p,d,q) .

ARIMA models can be estimated following the Box–Jenkins approach. The ARIMA model predicts a given time series based on its own past values. It can be used for any nonseasonal series of numbers that exhibits patterns and is not a series of random events. ARIMA forecasting is achieved by plugging in time series data for the variable of interest. Statistical software will identify the appropriate number of lags or amount of differencing to be applied to the data and check for stationarity. It will then output the results, which are often interpreted similarly to that of a multiple linear regression model.

ARIMA models are widely used in technical analysis to forecast future security prices. They are becoming a popular tool for data scientists to employ for forecasting future demand, such as sales forecasts, manufacturing plans, or stock prices. Accurate predictions can help lower costs and prevent significant disruption in the supply chain and production activities of a company[[4]](https://www.mastersindatascience.org/learning/statistics-data-science/what-is-arima-model...