Time Series

A time series is a sequence of observations indexed in time order. This poster covers the theoretical foundations of time series analysis and the practical tools for model identification.

Components of a Time Series

• Trend — long-run direction (upward, downward, flat)
• Seasonality — regular, calendar-driven patterns
• Cyclical — irregular, economy-driven fluctuations
• Irregular — random noise

Stationarity

A time series is stationary if its statistical properties (mean, variance, autocovariance) do not change over time. Most ARIMA-family models require stationarity.

• ADF test (Augmented Dickey–Fuller) — tests for a unit root
• KPSS test — tests the null of stationarity
• Differencing — common transformation to achieve stationarity

ACF & PACF Pattern Guide

The poster provides a visual guide to identifying the correct model order from the correlogram:

Pattern	Suggested model
ACF cuts off at lag q; PACF tails off	MA(q)
ACF tails off; PACF cuts off at lag p	AR(p)
Both tail off	ARMA(p, q)
ACF has slow decay	Non-stationary — difference first

ARIMA Model Types

• AR(p) — autoregressive: current value depends on past values
• MA(q) — moving average: current value depends on past errors
• ARMA(p, q) — combination of AR and MA
• ARIMA(p, d, q) — adds d rounds of differencing
• SARIMA — seasonal extension with additional (P, D, Q, s) terms