Arima
ARIMA is a statistical time-series model that combines autoregressive terms, differencing, and moving-average terms to represent temporal dependence and generate forecasts.
Statistics Every Programmer Needs
An ARIMA model is an autoregressive integrated moving-average time-series model that represents temporal dependence using autoregression, differencing, and moving averages.
- How it is used
- Forecasts time-ordered data by modeling dependence on past observations and errors after differencing.
- How deep it goes
- Defines the three components, selects an order through stationarity and correlation checks, fits a model, and evaluates residuals and held-out forecasts.
- Examples
- Fits ARIMA(1, 1, 0) to Apple closing prices through March 2024 and compares its April forecast with observed prices.
- What you can do after
- Apply it via Python statsmodels to fit an ARIMA model, forecast held-out observations, and inspect residuals.
Outlier Detection in Python
ARIMA is a time-series forecasting method that models a value using autoregression, differencing, and moving-average error terms.
- How it is used
- Uses forecasting errors to detect outliers in time-series data.
- How deep it goes
- Explains the intuition, fitting workflow, held-out prediction, and tuning need without deriving ARIMA internals.
- Examples
- Uses synthetic weekday-pattern data, a 60-point forecast, plotted quantiles, and a deliberately inserted outlier.
- What you can do after
- Apply it via Darts to fit forecasts, predict a held-out horizon, plot results, and inspect unusually large errors.
Related concepts
- forecastingkind of · Forecasting is the process of predicting future values or outcomes from information currently available, often including historical observations.
- generationuses · Generation is the computational production of outputs from supplied inputs or context, often by applying a model to produce predictions or new content.
- SARIMAincludes · SARIMA is a seasonal autoregressive integrated moving-average model for forecasting time series with recurring seasonal dependencies.
- autoregressive modelhas part · An autoregressive model represents or predicts each value in a sequence based on preceding values in that sequence.
- integrationhas part · Integration in ARIMA is the differencing operation used to remove nonstationary temporal structure from a time series.
- local averaginghas part · Local averaging is a smoothing technique that replaces values with arithmetic means computed from nearby observations within successive or sliding windows.
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