Time-Series Forecasting
Time-series forecasting predicts future values of a temporally ordered signal from its own past and covariates.
Order matters
Time-series data is ordered in time, and that order carries information that ordinary regression ignores. Forecasting predicts future values from history, exploiting autocorrelation, trend, and seasonality. The temporal structure also constrains how models must be evaluated: you can never let information from the future leak into training a model meant to predict it.
Components of a series
- Trend: slow long-run drift up or down
- Seasonality: patterns that repeat on a fixed period (daily, weekly, yearly)
- Cycles: longer swings without a fixed period
- Noise: irreducible short-term fluctuation
Classical methods make these explicit. Seasonal decomposition splits a series into trend, seasonal, and remainder; exponential smoothing and ARIMA model them parametrically; additive decomposition models fit them as interpretable curves.
Evaluation without leakage
Random train-test splits are invalid because they let the model peek at the future. Instead, use a chronological split or rolling-origin backtesting, where the model is repeatedly trained on data up to a cutoff and tested on the next window. Report horizon-appropriate error: MAE, RMSE, or scale-free measures like MAPE and MASE that let you compare across series of different magnitudes.
Point forecasts and intervals
A single number is rarely enough; decisions need uncertainty. Good forecasters output prediction intervals, and those intervals should be calibrated, meaning a stated 90 percent interval actually contains the truth about 90 percent of the time. Deep models (recurrent and transformer sequence models) add capacity for many related series and exogenous inputs, but they must clear the same leakage-free evaluation bar as simple baselines like seasonal-naive, which are surprisingly hard to beat.