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arch: ARCH for Python

repository·main·Indexed 23 days ago

https://github.com/bashtage/arch

A Python library for financial econometrics specializing in Autoregressive Conditional Heteroskedasticity (ARCH) models and volatility modeling. Core capabilities include univariate volatility models (GARCH, TARCH, EGARCH, EWMA), unit root tests (ADF, Phillips-Perron, KPSS), cointegration analysis, long-run covariance estimation using HAC kernels like Bartlett, and various bootstrap methods (IID, Stationary, Circular Block, Moving Block) for confidence interval construction.

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What's inside arch

  1. Overview of arch capabilities

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    The arch library is a specialized toolkit for financial econometrics in Python. Its core capabilities include:

    • Volatility Modeling: Univariate models including ARCH, GARCH, TARCH, EGARCH, and EWMA/RiskMetrics, with support for various mean models and error distributions.
    • Unit Root Tests: Tests for stationarity such as Augmented Dickey-Fuller, Phillips-Perron, KPSS, and Zivot-Andrews.
    • Cointegration Analysis: Testing for cointegration (Engle-Granger, Phillips-Ouliaris) and estimating cointegration vectors (DOLS, FMOLS).
    • Bootstrapping: Various block bootstrap methods for covariance estimation and confidence interval construction.
    • Multiple Comparison Procedures: Tools like Model Confidence Set (MCS) and Test of Superior Predictive Ability (SPA).
    • Long-run Covariance Estimation: Kernel-based estimators like the Bartlett (Newey-West) kernel.

  2. Overview of the arch.bootstrap module

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    The arch.bootstrap module provides high-level and low-level interfaces for bootstrapping data. It supports data contained in NumPy arrays, pandas Series, or pandas DataFrames. All bootstrap methods in this module share a consistent interface, differing only in their specific names, setup parameters, and internal sampling schemes.

  3. Overview of the ARCH toolbox capabilities

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    The arch package is a Python toolbox designed for financial data analysis. It provides specialized routines for modeling volatility, statistical testing, and resampling methods.

    Key capabilities include:

    • Univariate volatility models: Modeling time-varying volatility in single time series.
    • Bootstrapping: Resampling methods for statistical inference.
    • Multiple comparison procedures: Adjusting for multiple testing problems.
    • Unit root tests: Testing for stationarity in time series.
    • Cointegration Testing and Estimation: Analyzing long-term relationships between non-stationary series.
    • Long-run covariance estimation: Estimating covariance matrices for time series data.

  4. Perform Cointegration Analysis and Vector Estimation

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    The arch.unitroot module extends single-series testing to multiple series via cointegration testing and cointegrating vector estimation.

    Cointegration Testing

    Use these to test for the existence of a cointegrating relationship between multiple series:

    • arch.unitroot.cointegration.engle_granger (Engle-Granger Test)
    • arch.unitroot.cointegration.phillips_ouliaris (Phillips-Ouliaris Tests)

    Cointegrating Vector Estimation

    Use these to estimate the cointegrating vector once a relationship is identified:

    • arch.unitroot.cointegration.DynamicOLS (Dynamic OLS)
    • arch.unitroot.cointegration.FullyModifiedOLS (Fully Modified OLS)
    • arch.unitroot.cointegration.CanonicalCointegratingReg (Canonical Cointegrating Regression)

  5. Specify univariate volatility models with arch.univariate

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    The arch.univariate module provides two ways to specify univariate volatility models:

    1. High-level API: Use arch_model to quickly specify a model by providing the data and model type. This is the recommended approach for most users.
    2. Low-level API: Use specific mean and volatility model methods (detailed in the mean-models section) for more granular control over model specification.

    Once a model is specified, you can generate forecasts using:

    • Analytical methods: When the model is mathematically tractable.
    • Simulation-based methods: Using Monte Carlo simulation or residual Bootstrap.

  6. Perform Unit Root Tests with arch.unitroot

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    The arch.unitroot module provides several statistical tests to check for the presence of a unit root in a time series. These tests help determine if a series is stationary or non-stationary.

    Available test implementations include:

    • ADF: Augmented Dickey-Fuller test.
    • DFGLS: Dickey-Fuller GLS test.
    • PhillipsPerron: Phillips-Perron test.
    • ZivotAndrews: Zivot-Andrews test (for structural breaks).
    • VarianceRatio: Variance ratio test.
    • KPSS: Kwiatkowski-Phillips-Schmidt-Shin test.

  7. Perform Unit Root Testing with arch.unitroot

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    The arch.unitroot module provides routines to determine if a time series is stationary or contains a unit root.

    Most tests in this module (ADF, DFGLS, Phillips-Perron, and Zivot-Andrews) assume a null hypothesis of a unit root and an alternative of a stationary process.

    However, the KPSS test is an exception: it assumes a null hypothesis of a stationary process with an alternative of a unit root.

  10. Use the bootstrap framework in ARCH v1.1

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    Version 1.1 introduced a general-purpose bootstrap framework. You can interact with this framework in two ways:

    1. High-level functions: Use functions like conf_int (for confidence intervals) or cov (for covariance estimation) which utilize the bootstrap framework internally.
    2. Low-level iteration: Use the bootstrap function directly as an iterator for custom bootstrap procedures.