Time Series Data: Structure and Concepts

Core Idea

Time series data records observations on a single unit at sequential, equally spaced time points — GDP, unemployment, or stock prices over quarters or years. Unlike cross-sectional data, time series observations are ordered and typically autocorrelated: past values predict future values. Standard OLS assumptions break down because errors are serially correlated and many economic variables have stochastic trends. Time series analysis requires specialized tools to account for the time dependence structure, distinguish short-run dynamics from long-run relationships, and handle non-stationary processes.

How It's Best Learned

Plot GDP and the federal funds rate over several decades, visually identifying trends, recessions (business cycles), and co-movement — this builds intuition before formalizing with AR models and cointegration.

Common Misconceptions

• A 'spurious regression' can show high R² and significant t-statistics between two trending but unrelated series — non-stationarity inflates test statistics.
• 'Seasonal adjustment' is a data preprocessing step, not a modeling technique; always clarify whether a series is seasonally adjusted before modeling.

Explainer

In cross-sectional data, each observation is an independent draw: one observation on household 47 tells you nothing about household 48. Time series data breaks this assumption. GDP in Q3 is strongly predicted by GDP in Q2, which was predicted by Q1. This temporal dependence — autocorrelation — is not a nuisance; it is the defining feature of time series data and must be modeled explicitly rather than ignored.

Most macroeconomic time series have a trend: they tend to grow over time (GDP, price levels) or fluctuate around a persistent level (interest rates, unemployment). This creates non-stationarity — the statistical properties of the series (mean, variance) change over time. A stationary series has a constant mean and variance that it returns to after any shock. A non-stationary series, by contrast, wanders without reversion. The difference matters enormously for what statistical tools are valid.

The most dangerous pitfall is spurious regression. If you regress two non-stationary series on each other — even if they are completely unrelated — you will typically find high R² and statistically significant coefficients. Both series share a common time trend, and OLS interprets that shared drift as evidence of a relationship. Before running any regression with time series data, you must test whether the series are stationary; if not, you need to either difference the data or use cointegration methods.

Trends can be deterministic (a fixed formula like t or t²) or stochastic (a random walk, where shocks permanently accumulate). The distinction matters for how you remove the trend. For a deterministic trend, you can include a time trend variable in the regression. For a stochastic trend (unit root), you need to first-difference the data. Misdiagnosing the type of trend leads to incorrect detrending and invalid inference.

Time series also exhibit seasonality — regular patterns at fixed intervals (retail sales peak in December, agricultural output peaks at harvest). Seasonality is typically handled by seasonal differencing or adding seasonal dummy variables, or by working with seasonally adjusted data published by statistical agencies. Understanding whether a series is "raw" or "seasonally adjusted" is one of the first things to check before modeling.