Low-level Interfaces
--------------------

Constructing Parameter Estimates
================================
The bootstrap method apply can be use to directly compute parameter estimates
from a function and the bootstrapped data.

This example makes use of monthly S&P 500 data.

.. code-block:: python

    import datetime as dt

    import pandas as pd
    import pandas_datareader.data as web

    start = dt.datetime(1951, 1, 1)
    end = dt.datetime(2014, 1, 1)
    sp500 = web.DataReader('^GSPC', 'yahoo', start=start, end=end)
    low = sp500.index.min()
    high = sp500.index.max()
    monthly_dates = pd.date_range(low, high, freq='M')
    monthly = sp500.reindex(monthly_dates, method='ffill')
    returns = 100 * monthly['Adj Close'].pct_change().dropna()

The function will compute the Sharpe ratio -- the (annualized) mean divided by
the (annualized) standard deviation.

.. code-block:: python

    import numpy as np
    def sharpe_ratio(x):
        return np.array([12 * x.mean() / np.sqrt(12 * x.var())])

The bootstrapped Sharpe ratios can be directly computed using `apply`.

.. code-block:: python

    import seaborn
    from arch.bootstrap import IIDBootstrap
    bs = IIDBootstrap(returns)
    sharpe_ratios = bs.apply(sr, 1000)
    sharpe_ratios = pd.DataFrame(sharp_ratios, columns=['Sharpe Ratio'])
    sharpe_ratios.hist(bins=20)

.. image:: bootstrap_histogram.png


The Bootstrap Iterator
======================
The lowest-level method to use a bootstrap is the iterator.  This is used
internally in all higher-level methods that estimate a function using multiple
bootstrap replications.  The iterator returns a two-element tuple where the
first element contains all positional arguments (in the order input) passed when
constructing the bootstrap instance, and the second contains the all keyword
arguments passed when constructing the instance.

This example makes uses of simulated data to demonstrate how to use the
bootstrap iterator.

.. code-block:: python

    import pandas as pd
    import numpy as np

    from arch.bootstrap import IIDBootstrap

    x = np.random.randn(1000, 2)
    y = pd.DataFrame(np.random.randn(1000, 3))
    z = np.random.rand(1000, 10)
    bs = IIDBootstrap(x, y=y, z=z)

    for pos, kw in bs.bootstrap(1000):
        xstar = pos[0]  # pos is always a tuple, even when a singleton
        ystar = kw['y']  # A dictionary
        zstar = kw['z']  # A dictionary