Moving average or running mean

python

numpy

pandas

performance

byAnton Shumikhin·Nov 24, 2024

For rapidly computing a moving average in Python, numpy library's numpy.convolve has you covered. Let's say you wish to smoothen your data with a window size of 3:

import numpy as np

data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]  # Preparing for smoothness application.
window = 3  # Window size for a smoother ride.

# Pass me the smoothing cream!
smoothed = np.convolve(data, np.ones(window)/window, 'valid')  

print(smoothed)  # Ta-da! Smooth as a baby's bottom.

This spits out the smoothed data, clipping edges to get results from fully filled window overlaps.

Understanding numpy.convolve

Using a candle to light another, numpy.convolve applies convolution to calculate the moving average, effectively offering a way to apply weight distribution across a window. The choice of mode='valid' in np.convolve is like choosing VIP seating in a concert. You avoid unnecessary distractions (edge-effects here), focusing only where full-windows are available.

Enhanced alternatives

For those who love extra dressing on their salad, scipy.ndimage.uniform_filter1d is a burly alternative recipe for handling larger arrays or varying window sizes. Remember, bigger isn't always better, but in this case, it kinda is.

from scipy.ndimage import uniform_filter1d

# New smoothness generator in town.
smoothed = uniform_filter1d(data, size=window)

If finance is your jam, consider the James Bond of technical analysis libraries, talib. Offering a range of sophisticated functions, it charts a cunning path to calculating moving averages even with shaken (well, shaken data) input.

import talib

# Financial data always has a seat at the cool table.
smoothed = talib.MA(np.array(data), window)

Traps Along the Way: precision and edge handling

Coding a running mean is like walking a tightrope. There's always the danger of floating-point precision errors causing low-key slips. Use np.longdouble as your safety net. It won't stop falls, but it might make them less painful.

cumulative_sum = np.cumsum(np.longdouble(data))
smoothed = (cumulative_sum[window - 1:] - cumulative_sum[:-window]) / window  # Smooth, isn't it?

Also, special Oracles called edge cases can often lead you off the path. Libraries like Pandas, offering methods like pandas.Series.rolling.mean(), are decent guides through these treacherous terrains.

Performance and dealing with large datasets

Remember that compression scene in Star Wars? Vectorized operations can save you from similar spots when dealing with large arrays. Functions from numpy and pandas are like Luke Skywalker's lightsaber in such situations - swift and effective.

Also, your design should be as adaptive as a chameleon so it doesn't bat an eyelid at different window sizes.

Advanced libraries and Research Links

There's always a bigger fish. For peak performance (beyond what even numpy and pandas deliver), specialized libraries like talib, Cython or C extensions may be your droids, er, tools of choice.

I've also laid out a bread crumb trail for you (see references section). Deep insights into error analysis and performance comparisons await your visit.

Transients and Preserving Arrays

Starting Transient: The Phantom Menace

That sneaky part at the start of your signal, where the window hasn't filled up, is the 'starting transient'. It's like a light beer – not quite there yet. But convolve has got you covered. You can either trim the start or react cleverly to the incomplete windows:

full_window = np.convolve(data, np.ones(window)/window, 'same')  # Same same, but different.
smoothed = full_window[window - 1:]  # Trim the beer belly.

Preserving that Original Size

Maybe you're the sentimental type and want to hold on to that original array size. No problem – just use np.insert before the cumsum, and you're golden:

padded_data = np.insert(data, 0, [0]*window)  # Adding some extra room.
cumulative_sum = np.cumsum(np.longdouble(padded_data))
smoothed = (cumulative_sum[window:] - cumulative_sum[:-window]) / window  
smoothed = smoothed[:len(data)]  # Back to basics.