> For the complete documentation index, see [llms.txt](https://ondrej-kvasnovsky-2.gitbook.io/handbook-of-hidden-data-scientist-python/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ondrej-kvasnovsky-2.gitbook.io/handbook-of-hidden-data-scientist-python/statistical-analysis/rolling-statistics.md).

# 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.

![](/files/-M3wYQTP6JZJAa7YoA0s)

## 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.

![](/files/-M3wYQTRaqhn3MT5Kqc0)

## 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.

![](/files/-M3wYQTTq8sCYzk2K0xc)