Time Series Analysis

Time series analysis handles data ordered chronologically, where temporal dependencies matter.

Ask the Data science assistant 1 min read · Updated September 9, 2026

Definition

Key feature: autocorrelation — $y_t$ is correlated with $y_{t-1}$ , $y_{t-2}$ , etc. (unlike i.i.d. data).

Trends (long-term direction) and seasonality (cyclical patterns) are core components: $Y_t = T_t + S_t + R_t$ (additive) or multiplicative.

Intuition

Standard regression assumes independent observations — time series violates this, so standard errors and p-values are wrong if you ignore it.

The autocorrelation function (ACF) plots correlation vs. lag; the partial autocorrelation (PACF) controls for intermediate lags.

Worked example

Monthly retail sales: trend (growing over years) + seasonality (holiday spike in December) + remainder.

Stock prices are nearly random walk (autocorrelation near zero) — difficult to predict.

The math

ARIMA $(p,d,q)$ : autoregressive (AR) order $p$ , differencing order $d$ , moving-average order $q$ . $\nabla^d y_t$ is stationary and modeled as ARMA $(p,q)$ .

A time series is stationary if mean, variance, and autocorrelation are constant over time — differencing achieves this.

In practice

Used for demand forecasting, inventory planning, financial prediction, and anomaly detection in monitoring systems.

Modern methods (Prophet, Temporal Fusion Transformers) handle multiple seasonality and external regressors (holidays, promotions).

Go deeper

More in Data science

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.