Time Series Forecasting

Time Series Forecasting is the statistical modelling discipline that produces point and interval predictions of future values from chronologically ordered data (demand, price, temperature, traffic). Core components: trend (long-run direction), seasonality (periodic repetition), cycle (long-wave oscillation) and residual (noise). The classical methodology was formalised by Box and Jenkins (1970): stationarity tests (ADF, KPSS), differencing (d), autocorrelation (ACF) and partial autocorrelation (PACF) analysis, ARIMA (p,d,q) and SARIMA (P,D,Q,m) identification, parameter estimation and residual diagnostics. The state-space family (ETS — error/trend/seasonal) models trend and seasonality in a flexible framework; Holt-Winters triple exponential smoothing is a practical antecedent. Modern variants include structural time-series models, dynamic regression (ARIMAX with exogenous inputs), Bayesian time series and machine-learning approaches (gradient boosting, LSTM, Temporal Fusion Transformer). Hyndman and Khandakar (2008) standardised automatic model-selection methodology. For hierarchical forecasts (SKU to category to total), reconciliation methods enforce cross-level consistency.