Plot the ratio of the standard deviation to the mean over bandwidth

Question

I wanted to reveal hard to see correlation in data via computing the ratio of the standard deviation to the mean over the given bandwidth. The window would be shifted one frequency bin to the right, and the ratio is computed again, and so on. I thought it is possible with ready function from Matplotlib or scipy library? I would be very grateful for showing me the solution.

Answer 1

Solution

What you are trying to calculate is a rolling version of Relative Standard Deviation (RSD), which is also known as Coefficient of Variation (CV). See Wikipedia and Investopedia for more details on the definition.

RSD = CV = SD/Mean

Let us make some time-series data first.

import pandas as pd
import numpy as np

# some sample data
ts = pd.Series(np.random.randn(1000), 
               index=pd.date_range('1/1/2000', 
                                   periods=1000)).cumsum()

The following piece of code will give you what you need.

Option-A

window = 60
rolling_rsd = ts.rolling(window=window).std()/ts.rolling(window=window).mean()

Option-B

Or, you could use this convenience function:

def rsd(ts, window = 60):
    """
    Returns the Relative Standard Deviation (RSD), 
    a.k.a Coefficient of Variation (CV) for a 
    given rolling window size on a time series data-column.
    
    ts = time series data
    window = window size to compute rolling mean, std, rsd
    Example:
       rolling_rsd, rolling_mean, rolling_std = rsd(ts, window = 60)
    """
    rolling_mean = ts.rolling(window=window).mean()
    rolling_std = ts.rolling(window=window).std()
    rolling_rsd = rolling_std/rolling_mean
    
    return (rolling_rsd, rolling_mean, rolling_std)

Detailed Example

I will use convenience function, rsd() for following example.

import pandas as pd
import numpy as np

# some sample data
ts = pd.Series(np.random.randn(1000), index=pd.date_range('1/1/2000', periods=1000)).cumsum()

#plot the time series
ts.plot(style='k--')

# Using convenience function: rsd()
# calculate rolling RSD, MEAN and STD with window = 60
(rolling_rsd, rolling_mean, rolling_std) = rsd(ts, window = 60)

# calculate a 60 day rolling mean and plot
rolling_mean.plot(style='k')

# add the 60 day rolling standard deviation (STD) to the plot
rolling_std.plot(style='b')

# add the 60 day rolling  relative standard deviation (RSD) to the plot
rolling_rsd.plot(style='r')

Note:

You could also just calculate this directly as follows (if you prefer not to use another function).

# calculate a 60 day rolling standard deviation (rsd)

rolling_rsd = ts.rolling(window=60).std()/ts.rolling(window=60).mean()

Related Solution/Question:

1. How can I simply calculate the rolling/moving variance of a time series in python?