Time Series

Basic theory and identification of ACF and PACF chart patterns, as well as ARIMA time series types.

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