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ARCH for Python

Project Description


This is a work-in-progress for ARCH and other tools for financial econometrics, written in Python (and Cython)


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.


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


### 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

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

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

   from arch import arch_model
   am = arch_model(returns)
   res =

### Unit Root Tests
  • Augmented Dickey-Fuller
  • Dickey-Fuller GLS
  • Phillips-Perron
  • KPSS
  • Variance Ratio tests

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

### 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.

   # Import data
   import datetime as dt
   import pandas as pd
   import as web
   start = dt.datetime(1951,1,1)
   end = dt.datetime(2014,1,1)
   sp500 = web.get_data_yahoo('^GSPC', start=start, end=end)
   start = sp500.index.min()
   end = sp500.index.max()
   monthly_dates = pd.date_range(start, end, freq='M')
   monthly = sp500.reindex(monthly_dates, 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.conf_int(sharpe_ratio, 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.


  • NumPy (1.7+)
  • SciPy (0.12+)
  • Pandas (0.14+)
  • statsmodels (0.5+)
  • matplotlib (1.3+)

Optional Requirements

  • Numba (0.15+) will be used if available and when installed using –no-binary


  • Cython (0.20+, if not using –no-binary)
  • nose (For tests)
  • sphinx (to build docs)
  • sphinx-napoleon (to build docs)

Note: Setup does not verify requirements. Please ensure these are installed.


pip install git+git://


Anaconda builds are not currently available for OSX.

conda install -c arch


With a compiler

If you are comfortable compiling binaries on Windows:

pip install git+git://

No Compiler

All binary code is backed by a pure Python implementation. Compiling can be skipped using the flag --no-binary

pip install git+git:// --install-option "--no-binary"

Note: the test suite compares the Numba implementations against Cython implementations of some recursions, and so it is not possible to run the test suite when installing with --no-binary .


conda install -c arch

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