DataTerminology.comNEW
A forecasting model combining autoregression, differencing, and moving averages for nonstationary time series.
DESCRIPTION
ARIMA models generalize ARMA by adding differencing to achieve stationarity before modeling autocorrelation and shocks. The three orders (p,d,q) specify autoregression, differencing, and moving average terms. Seasonal ARIMA (SARIMA) extends this with seasonal orders. Model identification typically uses ACF/PACF patterns and information criteria. Residual diagnostics ensure adequacy and guide refinements. ARIMA is effective for univariate forecasting with stable dynamics and limited exogenous effects.
ALTERNATIVE DEFINITIONS
Forecasting: Principles and Practice (Hyndman & Athanasopoulos)
An ARIMA(p,d,q) model is a generalisation of an ARMA(p,q) model to include differencing (the ‘I’ component) to make the series stationary.
Clarifies role of differencing in extending ARMA to ARIMA.
Wikipedia
In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model.
Positions ARIMA as a generalization of ARMA within time series analysis.
RELATED TERMS
Autoregressive Moving Average SARIMA Stationarity Differencing Autocorrelation Function Partial Autocorrelation Box–Jenkins Forecasting Residual Diagnostics Unit Root
COMPETING TERMS
Exponential Moving Average Prophet
RELATIONS
- Broader: Autoregressive Moving Average Forecasting
- Derived from: Autoregressive Moving Average
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst AI Engineer
EXTERNAL SOURCES
- Wikipedia - Autoregressive integrated moving average
- statsmodels - ARIMA class reference
- Penn State Eberly College of Science - ARIMA modeling course notes
TOP QUESTIONS
How do I choose ARIMA orders (p, d, q)?
Inspect stationarity to set d, then use ACF/PACF patterns and information criteria (AIC, BIC) to select p and q. Validate via residual diagnostics.
Category: How-to
When is ARIMA preferred over Exponential Smoothing?
ARIMA suits series with autocorrelated residual structures and stable dynamics. ETS often excels for strong trend/seasonality without complex autocorrelation.
Category: Opinion
What is SARIMA?
SARIMA extends ARIMA with seasonal AR, I, and MA components, modeling periodic behavior at seasonal lags (e.g., 12 for monthly).
Category: Concept
Can ARIMA handle exogenous regressors?
Yes, ARIMAX (or SARIMAX) includes exogenous variables to explain variation beyond autoregressive and moving average terms.
Category: Concept
What are common ARIMA pitfalls?
Over-differencing, ignoring residual autocorrelation, and neglecting seasonality. Poor diagnostics and short training windows also impair performance.
Category: Mistakes
How do I validate an ARIMA model?
Check residual white noise using Ljung–Box, inspect ACF/PACF of residuals, and perform out-of-sample forecast evaluation with rolling-origin cross-validation.
Category: How-to
Is ARIMA suitable for intermittent demand?
Typically no; Croston’s method or specialized intermittent models perform better. ARIMA assumes more continuous signal structures.
Category: Opinion
How does ARIMA compare to Prophet?
ARIMA is a stochastic, parametric model focusing on autocorrelation; Prophet is a decomposable model emphasizing trend, seasonality, and holidays with strong defaults.
Category: Comparison
Can ARIMA model non-linear dynamics?
ARIMA is linear. Non-linear patterns require extensions (e.g., TAR, GARCH for variance) or machine learning models.
Category: Limitations