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  "body": "\n## Summary\n\nAn autoregressive integrated moving average model, or ARIMA($p$, $d$, $q$) model, is a time series model whose $d$-th differences form an [[ARMA($p$, $q$) process|B1HNX0YT0Z]].\nIt extends ARMA models to non-stationary series with trends or random-walk behaviour.\nThe word \"integrated\" refers to undoing the differencing by summation.\nARIMA models are among the most widely used models for forecasting economic and business series.\n\n## Explanations\n\n### L1 human\n\nMany series, such as a stock price index, do not hover around a fixed level; they drift and wander.\nThe changes from one step to the next, however, often look stable.\nARIMA models fit an ARMA model to these changes, and then add the changes back up to forecast the series itself.\nThe simplest case is the random walk $X_t = X_{t-1} + \\varepsilon_t$, which is ARIMA($0$, $1$, $0$): its changes $X_t - X_{t-1} = \\varepsilon_t$ are pure noise.\n",
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