Time Series
Data indexed in time order, analyzed to find trends, cycles, and to forecast future values.
Definition
A time series is a sequence of observations recorded over time. Because order and timing carry information, time-series analysis uses methods that account for temporal dependence, unlike methods that assume independent samples.
Stationarity, whether a series' statistical properties stay constant over time, is a central assumption of many classical methods, and non-stationary data is often transformed by differencing before modeling. Diagnosing stationarity is a routine first step in time-series analysis.
What sets time series apart is temporal dependence: observations near in time are correlated, which violates the independence assumptions of ordinary statistics and demands specialized methods. Stationarity, whether the series' statistical properties hold constant, is a key assumption often achieved by differencing. Forecasting must also respect causality in evaluation, testing only on data that follows the training period, or it reports optimistic accuracy it could never achieve in deployment.
Components and tasks
- Trend, seasonality, and noise decomposition.
- Autocorrelation: dependence between nearby points.
- Forecasting future values (ARIMA, state-space, neural models).
- Anomaly detection in the stream.
Why it matters
Time-series analysis underlies forecasting in finance, weather, operations, and monitoring. Its central challenge is that observations are correlated in time, which violates the independence assumptions of ordinary statistics and demands specialized tools.
Fusion connection
Plasma diagnostics produce dense time series, and analyzing their temporal structure is key to understanding discharge evolution and anticipating instabilities in Hyperion simulations.