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Information Criteria (AIC/BIC)
Statistical metrics (Akaike Information Criterion and Bayesian Information Criterion) used to compare and select the best ARIMA models by penalizing model complexity to prevent overfitting.
Backshift (Lag Operator)
Mathematical operator denoted as B that shifts a time series backward by one period (B^k * Y_t = Y_{t-k}), fundamental for the compact notation of ARIMA and SARIMA models.
Forecasting
Application of a fitted ARIMA/SARIMA model to generate future values of the time series, accompanied by forecast intervals quantifying the associated uncertainty.
Residual Diagnostics
Analysis of forecast errors (residuals) from an ARIMA model to verify the white noise assumption, using tests like Ljung-Box and ACF/PACF plots of residuals.
ARMAX Model
Extension of the ARIMA model that incorporates exogenous variables in addition to autoregressive and moving average components, denoted as ARMAX, to improve forecast accuracy.
Box-Jenkins Decomposition
Systematic methodology for ARIMA modeling, including identification (via ACF/PACF), estimation, validation (residual diagnostics), and forecasting, popularized by Box and Jenkins.
SARIMAX
SARIMA model extended with exogenous variables, combining seasonal and non-seasonal components with external predictors for more comprehensive time series modeling.
Ljung-Box Test
Statistical test used in ARIMA model diagnostics to check if residuals exhibit significant autocorrelation, with a null hypothesis of no autocorrelation indicating an adequate model.