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# ARCH

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

## Module Contents

* [Univariate ARCH Models](#volatility)
* [Unit Root Tests](#unit-root)
* [Bootstrapping](#bootstrap)
* [Multiple Comparison Tests](#multiple-comparison)

## Documentation

Released documentation is hosted on
[read the docs](http://arch.readthedocs.org/en/latest/).
Current documentation from the master branch is hosted on
[my github pages](http://bashtage.github.io/arch/doc/index.html).

## More about ARCH

More information about ARCH and related models is available in the notes and
research available at [Kevin Sheppard's site](http://www.kevinsheppard.com).

## 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

<a name="volatility"/>

### 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](http://nbviewer.ipython.org/github/bashtage/arch/blob/master/examples/univariate_volatility_modeling.ipynb) for a more complete overview.

```python
import datetime as dt
import pandas.io.data 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 = am.fit()
```

<a name="unit-root"/>

### Unit Root Tests

* Augmented Dickey-Fuller
* Dickey-Fuller GLS
* Phillips-Perron
* KPSS
* Variance Ratio tests

See the [unit root testing example notebook](http://nbviewer.ipython.org/github/bashtage/arch/blob/master/examples/unitroot_examples.ipynb) for examples of testing series for unit roots.

<a name="bootstrap"/>

### 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](http://nbviewer.ipython.org/github/bashtage/arch/blob/master/examples/bootstrap_examples.ipynb) 
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 pandas.io.data 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')
```

<a name="multiple-comparison"/>

### 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](http://nbviewer.ipython.org/github/bashtage/arch/blob/master/examples/multiple-comparison_examples.ipynb)
for examples of the multiple comparison procedures.

## Requirements

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

* Python (2.7, 3.5 - 3.7)
* NumPy (1.13+)
* SciPy (0.19+)
* Pandas (0.21+)
* statsmodels (0.8+)
* matplotlib (2.0+)

### Optional Requirements

* Numba (0.35+) will be used if available **and** when installed using
  the --no-binary option
* IPython (5.0+) is required to run the notebooks

### Installing

* Cython (0.24+, if not using --no-binary)
* py.test (For tests)
* sphinx (to build docs)
* guzzle_sphinx_theme (to build docs)
* ipython (to build docs)
* numpydoc (to build docs)

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

### Linux/OSX

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

#### Anaconda

_Anaconda builds are not currently available for OSX._

```bash
conda install arch -c bashtage
```

### Windows

Building extension using the community edition of Visual Studio is
well supported for Python 3.5+.  Building extensions for 64-bit Windows
for use in Python 2.7 is also supported using Microsoft Visual C++
Compiler for Python 2.7.  Building on other combinations of Python/Windows
is more difficult and is not necessary when Numba is installed since
just-in-time compiled code (Numba) runs as fast as ahead-of-time
compiled extensions.

#### With a compiler

If you are comfortable compiling binaries on Windows:

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

#### No Compiler

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

```bash
pip install git+https://github.com/bashtage/arch.git --install-option "--no-binary"
```

*Note*: If Cython is not installed, the package will be installed as-if
--no-binary was used.