# Time Series Basics

> Market data is a time series: values ordered in time. Learn the components of a time series, why order matters, returns vs prices and the core tools for analysis.

Source: https://learn.tradelabsai.com/math/time-series-basics/  
Track: Math and Statistics · Level: Advanced · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Time Series Basics", https://learn.tradelabsai.com/math/time-series-basics/

A time series is a sequence of data points ordered in time: daily closing prices, minute by minute volumes, monthly inflation figures. Almost all market data is time series data. Unlike a random sample, the order matters: today's value may depend on yesterday's, volatility can cluster and patterns can change over time. Time series analysis provides tools to describe, model and forecast this kind of data, and to avoid mistakes that come from treating it as a simple list of numbers.

## Components of a time series

| Component | Description | Market example |
|---|---|---|
| Trend | Long term upward or downward movement | Rising stock market over decades |
| Seasonality | Regular calendar patterns | Natural gas demand, retail sales. See [Seasonality in Commodities](https://learn.tradelabsai.com/commodities/seasonality-in-commodities/) |
| Cycles | Longer, irregular ups and downs | Business cycles. See [Business and Economic Cycles](https://learn.tradelabsai.com/macro/business-and-economic-cycles/) |
| Noise | Random, unpredictable variation | Day to day price fluctuations |

Decomposing a series into these parts helps separate signal from noise.

## Prices vs returns

Prices usually trend and wander without returning to a fixed level, making them non stationary. Returns (percentage or log changes) are much closer to stationary: their average and variance are more stable over time. Most statistical analysis is therefore done on returns, not prices. See [Stationarity, Differencing and Unit Roots](https://learn.tradelabsai.com/math/stationarity/) and [Lognormal Distribution](https://learn.tradelabsai.com/math/lognormal-distribution/).

**Example: Why returns, not prices**
Two unrelated stocks both trend upward over ten years. A correlation of their prices might be 0.9, suggesting a strong link. The correlation of their daily returns might be only 0.1. The price correlation was an artefact of both trending, not a real relationship. Using returns avoids this spurious result. See [Covariance and Correlation](https://learn.tradelabsai.com/math/covariance-and-correlation/).

## Key properties to check

| Property | Question | Lesson |
|---|---|---|
| Stationarity | Do the mean and variance stay stable? | [Stationarity, Differencing and Unit Roots](https://learn.tradelabsai.com/math/stationarity/) |
| Autocorrelation | Is today related to yesterday? | [Autocorrelation and Partial Autocorrelation](https://learn.tradelabsai.com/math/autocorrelation/) |
| Volatility clustering | Do big moves follow big moves? | [GARCH](https://learn.tradelabsai.com/math/garch/) |
| Structural breaks | Did the behaviour change at some point? | [Structural Breaks and Regime Changes](https://learn.tradelabsai.com/math/regime-changes/) |
| Seasonality | Are there calendar patterns? | |

## Basic tools

| Tool | Use |
|---|---|
| Moving averages | Smooth noise and show trends. See [Moving Averages Explained](https://learn.tradelabsai.com/indicators/moving-averages-explained/) |
| Rolling statistics | Track changing mean, volatility and correlation. See [Rolling and Expanding Windows](https://learn.tradelabsai.com/math/rolling-and-expanding-windows/) |
| Autocorrelation function (ACF) | Measures correlation with past values |
| Differencing | Turns trending series into changes |
| Decomposition | Splits a series into trend, seasonal and residual parts |
| Models | ARIMA for the mean, GARCH for volatility. See [ARIMA](https://learn.tradelabsai.com/math/arima/) and [GARCH](https://learn.tradelabsai.com/math/garch/) |

## Time series pitfalls

- **Look ahead bias:** using future information to calculate today's values, for example with a centred moving average or a full sample normalisation. See [Look-Ahead Bias](https://learn.tradelabsai.com/research/look-ahead-bias/).
- **Overlapping returns:** using rolling multi day returns creates artificial autocorrelation.
- **Non synchronous data:** markets in different time zones close at different times. See [Timestamps, Time Zones and Daylight Saving](https://learn.tradelabsai.com/programming/timestamps-and-time-zones/).
- **Data snooping:** testing many patterns on the same history. See [P-Hacking and Multiple Testing](https://learn.tradelabsai.com/research/p-hacking-and-multiple-testing/).
- **Changing regimes:** relationships that held in the past may break.

## Forecasting realities

Short term returns of liquid assets are very hard to forecast; they are close to random. Volatility, however, is much more predictable because it clusters. This is why many quantitative models focus on forecasting risk rather than direction, or look for small, persistent edges across many assets. See [White Noise and Random Walks](https://learn.tradelabsai.com/math/white-noise-and-random-walks/).

## Frequently asked questions

### What is a time series?

A sequence of data points recorded in time order, such as daily prices or monthly economic data.

### Why do traders analyse returns instead of prices?

Because returns are closer to stationary, with more stable statistical properties, while prices trend and can create misleading correlations.

### What are the components of a time series?

Trend, seasonality, cycles and random noise.

Next, learn the benchmark for randomness in [White Noise and Random Walks](https://learn.tradelabsai.com/math/white-noise-and-random-walks/).

## Continue learning

- Next lesson: [White Noise and Random Walks](https://learn.tradelabsai.com/math/white-noise-and-random-walks/)
- Previous lesson: [Empirical and Mixture Distributions](https://learn.tradelabsai.com/math/mixture-distributions/)
- Related: [Empirical and Mixture Distributions](https://learn.tradelabsai.com/math/mixture-distributions/): A mixture distribution blends several distributions, such as calm and volatile regimes. Learn how mixtures create fat tails, how they are fitted and their uses.
- Related: [White Noise and Random Walks](https://learn.tradelabsai.com/math/white-noise-and-random-walks/): A random walk is a path built from random steps; white noise is pure randomness. Learn how they model prices, the random walk hypothesis and the evidence against it.
- Related: [Autocorrelation and Partial Autocorrelation](https://learn.tradelabsai.com/math/autocorrelation/): Autocorrelation measures how a series relates to its own past values. Learn the formula, the ACF, what positive and negative autocorrelation mean and why it matters.
- Related: [Stationarity, Differencing and Unit Roots](https://learn.tradelabsai.com/math/stationarity/): A stationary series has stable statistical properties over time. Learn why prices are non stationary, how to test with ADF and KPSS and how to make data stationary.
- Related: [ARIMA](https://learn.tradelabsai.com/math/arima/): ARIMA models forecast a time series from its own past values and errors. Learn the AR, I and MA terms, how to choose orders and why returns are hard to predict.
- Related: [Rolling and Expanding Windows](https://learn.tradelabsai.com/math/rolling-and-expanding-windows/): Rolling windows use a fixed recent period; expanding windows use all data so far. Learn when to use each, window length trade offs and how to avoid look ahead bias.