.. _ts-what-are-time-series-and-how-are-they-used: ======================================================================== What Are Time Series, and How Are They Used? ======================================================================== **Stage 1 · 🧭 Orientation** · Lesson 01 of 18 · *beginner* :doc:`Next · Getting Started with R ▶ <02-getting-started-with-r>` · :doc:`↑ Section ` .. important:: **✨ AI-generated content.** This page was written with the assistance of an AI language model and is provided as a learning aid. Despite careful review, it may still contain mistakes, omissions, or out-of-date information. Whether you are new to the topic, a team lead, or a senior practitioner, treat it as a starting point rather than an authoritative reference: read it critically and independently verify anything you act on (code, commands, figures, and factual claims) against official documentation and primary sources before relying on it. What it is ------------ A **time series** is a sequence of observations recorded **in time order**, usually at regular intervals — daily sales, hourly temperature, quarterly GDP. Written :math:`\{x_t\}` for :math:`t = 1, \dots, T`, its defining feature is that the **index is time** and the ordering is part of the data: each point is related to the ones before it. The moving parts ------------------ Classical analysis decomposes a series into a few recurring components: * **trend** — the long-run drift up or down; * **seasonality** — a **fixed-period** repeating pattern (weekly, monthly, yearly); * **cyclic** behaviour — wandering swings of **no fixed length**; * **residual / irregular** — the noise left once the rest is removed. ``statsmodels``' ``seasonal_decompose`` splits trend, seasonal and residual parts as an additive or multiplicative sum. A useful subtlety: a series with **cycles but no fixed-length seasonality** can still be stationary. Why order matters ------------------ Because neighbouring points are **dependent**, time series break the **i.i.d.** assumption most machine learning rests on. You cannot shuffle rows or use ordinary k-fold cross-validation — that leaks future information into the past. Order is not a nuisance here; it is the **signal** that makes forecasting possible at all. Where it's used ---------------- Two complementary goals recur across every domain: * **analysis** — understand the structure (trend, seasonality, autocorrelation); * **forecasting** — predict future values, ideally with uncertainty intervals. Typical applications include demand, price and capacity forecasting; monitoring and anomaly detection; economics and finance; weather and climate; and any sensor or telemetry stream. .. hint:: **Related lessons:** :doc:`A Gentle Introduction to Stationarity <03-a-gentle-introduction-to-stationarity>` · :doc:`Getting Started with R <02-getting-started-with-r>` · :doc:`ARIMA Models: How Nonstationary Models Are Built from Stationary Ones <15-arima-models-how-nonstationary-models-are-built-from-stationary-ones>` · :doc:`Exponential Smoothing Models <18-exponential-smoothing-models>` .. seealso:: **Source article** Adapted (context, re-expressed) in our own words from: `https://insightful-data-lab.com/2026/01/17/what-are-time-series-and-how-are-they-used/ `__ (insightful-data-lab.com). .. tags:: purpose: reference, topic: time series, level: beginner