arch

Autoregressive Conditional Heteroskedasticity (ARCH) and other tools for financial econometrics, written in Python (with Cython and/or Numba used to improve performance)

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Module Contents

• Univariate ARCH Models
• Unit Root Tests
• Cointegration Testing and Analysis
• Bootstrapping
• Multiple Comparison Tests
• Long-run Covariance Estimation

Python 3

arch is Python 3 only. Version 4.8 is the final version that supported Python 2.7.

Documentation

Documentation from the main branch is hosted on my github pages.

Released documentation is hosted on read the docs.

More about ARCH

More information about ARCH and related models is available in the notes and research available at Kevin Sheppard's site.

Contributing

Contributions are welcome. There are opportunities at many levels to contribute:

• Implement new volatility process, e.g., FIGARCH
• Improve docstrings where unclear or with typos
• Provide examples, preferably in the form of IPython notebooks

Examples

Volatility Modeling

• Mean models
  • Constant mean
  • Heterogeneous Autoregression (HAR)
  • Autoregression (AR)
  • Zero mean
  • Models with and without exogenous regressors
• Volatility models
  • ARCH
  • GARCH
  • TARCH
  • EGARCH
  • EWMA/RiskMetrics
• Distributions
  • Normal
  • Student's T
  • Generalized Error Distribution

See the univariate volatility example notebook for a more complete overview.

```python import datetime as dt import pandasdatareader.data as web st = dt.datetime(1990,1,1) en = dt.datetime(2014,1,1) data = web.getdatayahoo('^FTSE', start=st, end=en) returns = 100 * data['Adj Close'].pctchange().dropna()

from arch import archmodel am = archmodel(returns) res = am.fit() ```

Unit Root Tests

• Augmented Dickey-Fuller
• Dickey-Fuller GLS
• Phillips-Perron
• KPSS
• Zivot-Andrews
• Variance Ratio tests

See the unit root testing example notebook for examples of testing series for unit roots.

Cointegration Testing and Analysis

• Tests
  • Engle-Granger Test
  • Phillips-Ouliaris Test
• Cointegration Vector Estimation
  • Canonical Cointegrating Regression
  • Dynamic OLS
  • Fully Modified OLS

See the cointegration testing example notebook for examples of testing series for cointegration.

Bootstrap

• Bootstraps
  • IID Bootstrap
  • Stationary Bootstrap
  • Circular Block Bootstrap
  • Moving Block Bootstrap
• Methods
  • Confidence interval construction
  • Covariance estimation
  • Apply method to estimate model across bootstraps
  • Generic Bootstrap iterator

See the bootstrap example notebook for examples of bootstrapping the Sharpe ratio and a Probit model from statsmodels.

```python

Import data

import datetime as dt import pandas as pd import numpy as np import pandasdatareader.data as web start = dt.datetime(1951,1,1) end = dt.datetime(2014,1,1) sp500 = web.getdatayahoo('^GSPC', start=start, end=end) start = sp500.index.min() end = sp500.index.max() monthlydates = pd.daterange(start, end, freq='M') monthly = sp500.reindex(monthlydates, method='ffill') returns = 100 * monthly['Adj Close'].pct_change().dropna()

Function to compute parameters

def sharpe_ratio(x): mu, sigma = 12 * x.mean(), np.sqrt(12 * x.var()) return np.array([mu, sigma, mu / sigma])

Bootstrap confidence intervals

from arch.bootstrap import IIDBootstrap bs = IIDBootstrap(returns) ci = bs.confint(sharperatio, 1000, method='percentile') ```

Multiple Comparison Procedures

• Test of Superior Predictive Ability (SPA), also known as the Reality Check or Bootstrap Data Snooper
• Stepwise (StepM)
• Model Confidence Set (MCS)

See the multiple comparison example notebook for examples of the multiple comparison procedures.

Long-run Covariance Estimation

Kernel-based estimators of long-run covariance including the Bartlett kernel which is known as Newey-West in econometrics. Automatic bandwidth selection is available for all of the covariance estimators.

```python from arch.covariance.kernel import Bartlett from arch.data import nasdaq data = nasdaq.load() returns = data[["Adj Close"]].pct_change().dropna()

cov_est = Bartlett(returns ** 2)

Get the long-run covariance

covest.cov.longrun ```

Requirements

These requirements reflect the testing environment. It is possible that arch will work with older versions.

• Python (3.9+)
• NumPy (1.19+)
• SciPy (1.5+)
• Pandas (1.1+)
• statsmodels (0.12+)
• matplotlib (3+), optional

Optional Requirements

• Numba (0.49+) will be used if available and when installed without building the binary modules. In order to ensure that these are not built, you must set the environment variable ARCH_NO_BINARY=1 and install without the wheel.

shell export ARCH_NO_BINARY=1 python -m pip install arch

or if using Powershell on windows

powershell $env:ARCH_NO_BINARY=1 python -m pip install arch

• jupyter and notebook are required to run the notebooks

Installing

Standard installation with a compiler requires Cython. If you do not have a compiler installed, the arch should still install. You will see a warning but this can be ignored. If you don't have a compiler, numba is strongly recommended.

pip

Releases are available PyPI and can be installed with pip.

shell pip install arch

You can alternatively install the latest version from GitHub

bash pip install git+https://github.com/bashtage/arch.git

Setting the environment variable ARCH_NO_BINARY=1 can be used to disable compilation of the extensions.

Anaconda

conda users can install from conda-forge,

bash conda install arch-py -c conda-forge

Note: The conda-forge name is arch-py.

Windows

Building extension using the community edition of Visual Studio is simple when using Python 3.8 or later. Building is not necessary when numba is installed since just-in-time compiled code (numba) runs as fast as ahead-of-time compiled extensions.

Developing

The development requirements are:

• Cython (0.29+, if not using ARCHNOBINARY=1, supports 3.0.0b2+)
• pytest (For tests)
• sphinx (to build docs)
• sphinx-immaterial (to build docs)
• jupyter, notebook and nbsphinx (to build docs)

Installation Notes

1. If Cython is not installed, the package will be installed as-if ARCH_NO_BINARY=1 was set.
2. Setup does not verify these requirements. Please ensure these are installed.