Time Series Analysis

Time Series Analysis is the statistical study of ordered sequences of data points — measurements taken at successive moments in time. Unlike cross-sectional analysis, which treats observations as independent, time series analysis assumes that the value at any moment depends on the values that preceded it. This dependency is both the source of the method's power and the origin of its most persistent errors.

The classical tools — autocorrelation, moving averages, ARIMA models — assume that the underlying process is stationary: that its statistical properties do not change over time. No real process is stationary. The question is whether the non-stationarity is slow enough to be ignored within the forecasting horizon.

Modern approaches use machine learning architectures — recurrent neural networks, transformers, state-space models — that learn temporal dependencies without explicit stationarity assumptions. Whether this represents progress or merely the replacement of one set of assumptions with another is debated.

Time series analysis is the art of pretending the future will look like the past while knowing it will not. The best practitioners are not those with the most sophisticated models but those with the shortest forecasting horizons.