Forecasting/time series analysis

A time series is a sequence of observations indexed in time. Time-series analysis describes how that sequence changes, separates recurring structure from irregular variation and, where appropriate, forecasts future values with quantified uncertainty.

When to use it

Use time-series analysis when the order and spacing of observations matter—for example, daily demand, monthly revenue, hourly energy use or a market closing value. The method can describe trend, seasonality, cycles, abrupt changes and dependence between current and earlier observations.

It can support questions such as:

• How might economic or business performance evolve over the coming months?
• What production volume and inventory may be needed?
• Is a recent movement normal seasonal variation or a structural break?
• How uncertain is the forecast, and which decisions are sensitive to that uncertainty?

Use another design when there is too little history, the process has changed fundamentally or the main objective is to estimate the causal effect of an intervention.

Origins

Time-series methods developed across astronomy, economics, signal processing and statistics. Early researchers studied trends, periodicity and serial correlation; later work formalised autoregressive and moving-average processes. George Box and Gwilym Jenkins integrated model identification, estimation, diagnostic checking and forecasting into an influential practical workflow. Contemporary analysis includes exponential smoothing, state-space models, dynamic regression and machine-learning approaches, but the same discipline remains: respect temporal order and validate forecasts out of sample.

What it is

Time-series analysis treats observations as potentially dependent rather than interchangeable. A value today may be related to recent values, seasonal positions, external variables and shocks.

A useful decomposition distinguishes:

level:

the current baseline of the series;

trend:

sustained movement over time;

seasonality:

a pattern repeating at a known calendar or operational frequency;

cycle:

broader movement without a fixed seasonal period;

irregular variation:

shocks, noise and measurement error.

Forecasts extrapolate learned structure under explicit assumptions. They are conditional estimates, not predictions that the future will repeat the past exactly.