STA457: Time Series Analysis MOC

This map indexes every atomic note for STA457 along stationarity, classical decomposition, AR/MA/ARMA models, and forecasting.

Time Series Fundamentals

Core time series concepts.

• Time Series
• Stochastic Process vs Time Series
• Time Series Characteristics
• Stationarity
• Strict Stationarity
• Weak Stationarity
• Strict vs Weak Stationarity

Autocovariance and Autocorrelation

Autocovariance and autocorrelation functions.

• Autocovariance Function (ACVF)
• Autocorrelation Function (ACF)
• Sample ACF

Variance and Covariance Properties

Variance and covariance properties.

• Variance and Covariance Properties
• Independence vs Uncorrelatedness

White Noise and IID Processes

White noise and independent, identically distributed (i.i.d.) processes.

• White Noise Process
• IID Noise
• IID vs White Noise
• Testing Residuals — iid and White Noise

Correlation Concepts

Correlation-related ideas.

• q-correlated vs q-dependent

Classical Decomposition

Classical decomposition methods.

• Classical Decomposition
• Trend Estimation — Moving Average Filter
• Trend Estimation — Regression
• Trend Estimation — Exponential Smoothing
• Trend Elimination — Differencing
• Seasonality Estimation and Elimination

Linear Processes and Filters

Linear processes and linear filters.

• Linear Process
• Causal Linear Process
• Linear Filter
• Backshift Operator

Autoregressive Processes

Autoregressive (AR) processes.

• Autoregressive Process
• AR(1) — Random Walk
• AR(1) — Causal Case
• AR(1) — Non-causal Stationary Case
• AR(1) — Causality vs Stationarity Summary
• Prediction for Causal AR(p)

Moving Average Processes

Moving average (MA) processes.

• Moving Average Process
• MA(1) ACVF and ACF
• MA(2) ACVF and ACF
• MA(q) ACF Cutoff Property

ARMA Processes

Autoregressive moving average (ARMA) processes.

• ARMA Process
• ARMA(1,1) Causal Representation

Forecasting and Prediction

Forecasting and optimal prediction.

• Best Predictor — Conditional Expectation
• Best Linear Predictor
• Best Linear Predictor — General (Theorem 1.2)
• Best Linear Predictor — P_n X_{n+h}
• Forecasting
• AR Forecasting
• Prediction Error
• Prediction Error Properties
• Prediction Intervals

Reference Materials

• STA457 Notation Index
• STA457_FORMULA_INDEX
• AR(1) Three Regimes
• MA(q) Complete Analysis
• ARMA from Definition to Prediction
• Stationarity Verification Pipeline
• From Raw Series to Stationary Residuals
• Best Linear Prediction for Stationary Series
• Exam Pattern - Stationarity and ACVF Computation
• Exam Pattern - Best Linear Prediction
• Exam Pattern - Difference Operators and Seasonality

Last updated: 2026-04-01