Rolling Statistics

Rolling, e.g. moving average, means - we create a sliding window, e.g. 20 days, and calculate mean for each window separatelly.

What statistic to use in order to find when to buy stocks?

We need to find the biggest value from the mean. So, it is rolling standard deviation.

Bollinger bands ®

Add two more STD moved by some number. When the data crosses one of those curves, we should think about sale or buy.

Using pandas.stats.moments for time series data

"""Bollinger Bands."""

import os
import pandas as pd
import matplotlib.pyplot as plt


def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))


def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                              parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df


def plot_data(df, title="Stock prices"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    plt.show()


def get_rolling_mean(values, window):
    """Return rolling mean of given values, using specified window size."""
    return pd.rolling_mean(values, window=window)


def get_rolling_std(values, window):
    """Return rolling standard deviation of given values, using specified window size."""
    return pd.rolling_std(values, window=window)


def get_bollinger_bands(rm, rstd):
    """Return upper and lower Bollinger Bands."""
    upper_band = rm + (rstd * 2)
    lower_band = rm - (rstd * 2)
    return upper_band, lower_band


def test_run():
    # Read data
    dates = pd.date_range('2012-01-01', '2012-12-31')
    symbols = ['SPY']
    df = get_data(symbols, dates)

    # Compute Bollinger Bands
    # 1. Compute rolling mean
    rm_SPY = get_rolling_mean(df['SPY'], window=20)

    # 2. Compute rolling standard deviation
    rstd_SPY = get_rolling_std(df['SPY'], window=20)

    # 3. Compute upper and lower bands
    upper_band, lower_band = get_bollinger_bands(rm_SPY, rstd_SPY)

    # Plot raw SPY values, rolling mean and Bollinger Bands
    ax = df['SPY'].plot(title="Bollinger Bands", label='SPY')
    rm_SPY.plot(label='Rolling mean', ax=ax)
    upper_band.plot(label='upper band', ax=ax)
    lower_band.plot(label='lower band', ax=ax)

    # Add axis labels and legend
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    ax.legend(loc='upper left')
    plt.show()


if __name__ == "__main__":
    test_run()

Here is the chart with original data, mean, and upper and lower curves.