Time series analysis

Time series analysis

Time series data breaks the assumption most methods rely on: that observations are independent. Yesterday predicts today, patterns repeat seasonally, and the future must never leak into the past. Analyzing it correctly means respecting time's structure and its one-way arrow.

Method

1. Decompose into trend, seasonality, and residual. Most series are a long-term trend, plus repeating seasonal cycles (daily, weekly, yearly), plus noise. Separating them (visually first: see data-visualization) tells you what is driving the series and what to model. A "surprising spike" is often just the weekly or holiday pattern.
2. Respect autocorrelation. Observations near in time are correlated, which violates the independence that standard statistical tests and train/test splits assume. This is why you cannot randomly shuffle time series data and why naive confidence intervals are too narrow. Account for it (autocorrelation plots reveal the structure).
3. Split by time, never randomly. Train on the past, test on the future, in order. A random split lets the model peek at future points to predict past ones, producing a fantasy score that collapses in production (see train-test-discipline). Use walk-forward validation (expanding or rolling window) to estimate real forecast performance.
4. Guard against look-ahead leakage. Every feature must use only information available at prediction time: a rolling average must not include the current or future point, a "total for the month" must not be known mid-month. Look-ahead leakage is the signature time-series bug and it makes backtests lie (see feature-engineering-tabular's point-in-time rule).
5. Match the forecasting method to the series. Simple baselines first (last value, seasonal naive, moving average): often hard to beat and the honest yardstick (see ml-baselines). Then classical methods (exponential smoothing, ARIMA) for clear trend/seasonality, or ML/deep models for complex multi-series problems. Do not reach for an LSTM before beating the seasonal-naive baseline.
6. Handle the practical realities. Missing timestamps and irregular intervals (resample deliberately), regime changes and structural breaks (a pandemic, a launch: the past may not predict the future through them), and non-stationarity (differencing or detrending where methods require stationary input).

Boundaries

• Forecasts carry growing uncertainty the further out they go; report prediction intervals, not just point forecasts, and distrust confident long-horizon predictions (see statistical-inference).
• Correlation-in-time is still not causation; two series trending together (or a lag relationship) can be coincidence or a shared driver (see correlation-causation).
• Structural breaks defeat any model trained before them; monitor for them and know that no method forecasts through an unprecedented regime change (see drift-monitoring).