Time Series Forecasting

A time series contains ordered measurements whose dependence can carry predictive information. Forecasting models may use autoregressive structure, smoothing, decomposed trend and seasonality, or supervised learning with lagged features. External predictors are useful only if their values will be known or separately forecast at the required horizon. One-step and multi-step forecasts create different error behavior. Backtesting simulates historical prediction dates to assess performance without using the future. Forecasting is broader than fitting a curve through past observations: the model must produce future values under a clearly defined information set and account for changes in the process over time.

Check timestamp meaning, sampling frequency, gaps and revisions before modeling. Establish naive and seasonal-naive baselines, define the horizon and use rolling or expanding historical evaluations. Build lags and transformations inside each training window, choose an error measure suited to the decision and inspect errors across horizons and seasonal periods. Examine residual dependence and interval coverage. Deliver a forecast process that explains how inputs, retraining and exceptional events are handled, including when a human adjustment is recorded separately from the model output.

Randomly shuffling observations breaks the temporal evaluation boundary. Structural changes, unusual events and revised historical data can invalidate apparently stable patterns. Percentage errors can behave poorly around zero, and forecast intervals are conditional on modeling assumptions. Seasonality needs enough relevant history; adding more lags does not guarantee useful signal. Distinguish forecasts from causal explanations, and inspect whether external regressors are genuinely available at prediction time rather than retrospectively filled with their realized values.