Time Series Models for Trading

Time series models are essential tools for analyzing and forecasting financial data. This chapter covers key time series techniques for algorithmic trading, including stationarity testing, ARIMA, VAR, GARCH, cointegration, and pairs trading strategies.

Chapter Overview

Time series analysis provides the statistical foundation for understanding price dynamics, forecasting returns, modeling volatility, and identifying mean-reverting relationships between assets. These techniques are critical building blocks for quantitative trading strategies.

Sub-page Topics Covered
Diagnostics & Stationarity ADF test, KPSS test, decomposition, autocorrelation
ARIMA, VAR & GARCH ARIMA forecasting, VAR multivariate models, GARCH volatility
Cointegration & Pairs Trading Engle-Granger, Johansen test, spread analysis, pairs strategy

Time Series Analysis Workflow 

graph TD
    A[Raw Price Data] --> B[Stationarity Tests]
    B -->|Stationary| C[ACF / PACF Analysis]
    B -->|Non-Stationary| D[Differencing / Transforms]
    D --> B
    C --> E{Model Selection}
    E --> F[ARIMA Forecasting]
    E --> G[VAR Multivariate]
    E --> H[GARCH Volatility]
    A --> I[Cointegration Tests]
    I -->|Cointegrated| J[Spread Construction]
    J --> K[Half-Life Estimation]
    K --> L[Pairs Trading Signals]
    L --> M[Backtest & Evaluate]
    F --> N[Trading Decisions]
    G --> N
    H --> N

    classDef input fill:#1a3a5c,stroke:#0d2137,color:#e8e0d4
    classDef test fill:#2d5016,stroke:#1a3a1a,color:#e8e0d4
    classDef process fill:#5c3a1a,stroke:#3a2510,color:#e8e0d4
    classDef model fill:#6b2d5b,stroke:#4a1a3f,color:#e8e0d4
    classDef output fill:#8b4513,stroke:#5c2e0d,color:#e8e0d4
    classDef decision fill:#3a5c1a,stroke:#263d11,color:#e8e0d4

    class A input
    class B,I test
    class C,D,J,K process
    class E decision
    class F,G,H model
    class L,M,N output

    linkStyle default stroke:#4a5568,stroke-width:2px

Key Concepts

Most time series models assume stationarity – statistical properties that do not change over time. Always test for stationarity before fitting models like ARIMA or VAR.

Why Time Series Models Matter for Trading

  • Forecasting returns: ARIMA and VAR models provide statistical forecasts that can inform trading signals.
  • Volatility modeling: GARCH models capture volatility clustering and enable better risk management.
  • Statistical arbitrage: Cointegration analysis identifies pairs of assets whose price spread is mean-reverting, forming the basis of pairs trading.
  • Regime detection: Time series diagnostics help identify structural breaks and regime changes in market behavior.

Key Takeaways

  1. Stationarity is fundamental: Always test for stationarity before applying time series models.
  2. ARIMA for forecasting: Use ARIMA models to forecast univariate time series. Auto-selection helps find optimal parameters.
  3. VAR for multivariate analysis: VAR models capture relationships between multiple time series and test for Granger causality.
  4. GARCH for volatility: GARCH models are essential for volatility forecasting and risk management.
  5. Cointegration for pairs trading: Cointegration identifies pairs with long-term equilibrium relationships suitable for statistical arbitrage.
  6. Mean reversion: Pairs trading exploits mean reversion in spreads between cointegrated assets.
  7. Half-life matters: Shorter half-lives indicate faster mean reversion and more trading opportunities.
  8. Risk management: Always include transaction costs and use proper position sizing in pairs trading.

Next Steps

  • Explore advanced time series models (state-space models, regime-switching models)
  • Implement dynamic hedge ratio estimation
  • Add risk management layers (stop-loss, position limits)
  • Develop multi-pair portfolio optimization
  • Integrate with live trading systems

Notebook: Run the examples interactively in ml_models.ipynb

Source Code

Browse the implementation: puffin/models/

For more details, see the Puffin repository and explore the examples in the repository.

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