Forecasting Methods

• italic: Definition / About
• Bold: Property / Theorem
• Standard: Procedure / Example / Cheatsheet

Fundamentals

• Cross-section Data
• Time Series Data
• Pooled Data
• Stochastic Process
• Time Series Components
• Lag
• Univariate vs Multivariate Models

Stationarity and Moments

• Autocovariance and Autocorrelation
• Weakly Stationary
  • Theorem: Strict Stationary implies Weakly Stationary
• Strictly Stationary
  • Theorem: Strict Stationary implies Weakly Stationary
• Sample Autocorrelation (ACF)
• Correlogram
• Random Walk

Parametric Models

• General Linear Process
  • Property: Stationarity Condition for General Linear Process

Autoregressive (AR) Processes

• Autoregressive (AR) Process
• AR(1) Process Model
  • Property: Stationarity Condition for AR(1)
  • Property: ACF of AR(1)
  • Example: Explosive AR(1) Process
• Backshift Operator (B)
• AR Characteristic Equation
• AR(p) Process Model
  • Property: Stationarity Condition for AR(p)
  • Property: Yule-Walker Equations for AR(p)
  • Property: Variance of AR(p)

Moving Average (MA) Processes

• White Noise
• Moving Average Process (Stochastic)
• Moving Average Process (MA(q))
  • Property: ACF of MA(q)
• MA(1) Process Model
  • Property: Bounds of MA(1) Autocorrelation
  • Property: Non-uniqueness of MA(1) Model
  • Property: Invertibility Condition for MA(1)
• MA(2) Process Model

Mixed and Integrated Models (ARMA/ARIMA)

• ARMA(p,q) Process Model
• ARMA(1,1) Process Model
  • Property: Variance and ACF of ARMA(1,1)
• Rationale for Non-Stationary Models
• ARIMA(p,d,q) Model
  • ARIMA(p,1,q) Formulation
  • Property: Characteristic Polynomial of ARIMA(p,1,q)
  • Constant Term in ARIMA
  • IMA(d,q) Model
  • ARI(p,d) Model
  • IMA(1,1) Model
  • IMA(2,2) Model
  • ARI(1,1) Model
  • Procedure: Determining Weights for ARI(1,1)

Smoothing Methods

• Smoothing Methods Overview
• Naive Method
• Averaging Method
• Single Moving Average (SMA)
• Double Moving Average (DMA)
• Single Exponential Smoothing (SES)
• Double Exponential Smoothing (Holt’s Linear Trend)
• Holt-Winter Seasonal Method

Strategy and Estimation

• Forecasting Model Accuracy Measures
• Model Selection via Data Splitting
• Box-Jenkins Strategy
• Estimating Constant Mean
• Least Squares for Linear Trend Estimation
• Least Squares for Quadratic Trend Estimation

Trends and Transformations

• Stochastic vs Deterministic Trend
• Linear and Quadratic Deterministic Trends
• Seasonal Average Model
• Procedure: Differencing to Achieve Stationarity
• Procedure: Log Transformation for Variance Stabilization
• Procedure: Percentage Changes Transformation

Examples

• Economic and Natural Time Series Examples