Logo Questions Linux Laravel Mysql Ubuntu Git Menu
 

Weighted moving average in python

I have data sampled at essentially random intervals. I would like to compute a weighted moving average using numpy (or other python package). I have a crude implementation of a moving average, but I am having trouble finding a good way to do a weighted moving average, so that the values towards the center of the bin are weighted more than values towards the edges.

Here I generate some sample data and then take a moving average. How can I most easily implement a weighted moving average? Thanks!

import numpy as np
import matplotlib.pyplot as plt

#first generate some datapoint for a randomly sampled noisy sinewave
x = np.random.random(1000)*10
noise = np.random.normal(scale=0.3,size=len(x))
y = np.sin(x) + noise

#plot the data
plt.plot(x,y,'ro',alpha=0.3,ms=4,label='data')
plt.xlabel('Time')
plt.ylabel('Intensity')

#define a moving average function
def moving_average(x,y,step_size=.1,bin_size=1):
    bin_centers  = np.arange(np.min(x),np.max(x)-0.5*step_size,step_size)+0.5*step_size
    bin_avg = np.zeros(len(bin_centers))

    for index in range(0,len(bin_centers)):
        bin_center = bin_centers[index]
        items_in_bin = y[(x>(bin_center-bin_size*0.5) ) & (x<(bin_center+bin_size*0.5))]
        bin_avg[index] = np.mean(items_in_bin)

    return bin_centers,bin_avg

#plot the moving average
bins, average = moving_average(x,y)
plt.plot(bins, average,label='moving average')

plt.show()

The output: Data and moving average

Using the advice from crs17 to use "weights=" in the np.average function, I came up weighted average function, which uses a Gaussian function to weight the data:

def weighted_moving_average(x,y,step_size=0.05,width=1):
    bin_centers  = np.arange(np.min(x),np.max(x)-0.5*step_size,step_size)+0.5*step_size
    bin_avg = np.zeros(len(bin_centers))

    #We're going to weight with a Gaussian function
    def gaussian(x,amp=1,mean=0,sigma=1):
        return amp*np.exp(-(x-mean)**2/(2*sigma**2))

    for index in range(0,len(bin_centers)):
        bin_center = bin_centers[index]
        weights = gaussian(x,mean=bin_center,sigma=width)
        bin_avg[index] = np.average(y,weights=weights)

    return (bin_centers,bin_avg)

Results look good: Working weighted average using numpy

like image 266
DanHickstein Avatar asked Aug 29 '13 17:08

DanHickstein


People also ask

What is weighted average in Python?

Syntax: def weighted_average(dataframe, value, weight): val = dataframe[value] wt = dataframe[weight] return (val * wt).sum() / wt.sum() It will return the weighted average of the item in value. In the numerator, we multiply each value with the corresponding weight associated and add them all.

How do you code moving averages in Python?

Method 1: Using Numpy It provides a method called numpy. cumsum() which returns the array of the cumulative sum of elements of the given array. A moving average can be calculated by dividing the cumulative sum of elements by window size.

What is a weighted moving average?

Weighted Moving Average (WMA) A Weighted Moving Average puts more weight on recent data and less on past data. This is done by multiplying each bar's price by a weighting factor. Because of its unique calculation, WMA will follow prices more closely than a corresponding Simple Moving Average.

How do you calculate exponential weighted moving average in Python?

To calculate exponential weights moving averages in Python, we can use the pandas ewm() function.


2 Answers

You could use numpy.average which allows you to specify weights:

>>> bin_avg[index] = np.average(items_in_bin, weights=my_weights)

So to calculate the weights you could find the x coordinates of each data point in the bin and calculate their distances to the bin center.

like image 60
crs17 Avatar answered Oct 22 '22 20:10

crs17


This won't give an exact solution, but it will make your life easier, and will probably be good enough... First, average your samples in small bins. Once you have resampled your data to be equispaced, you can use stride tricks and np.average to do a weighted average:

from numpy.lib.stride_tricks import as_strided

def moving_weighted_average(x, y, step_size=.1, steps_per_bin=10,
                            weights=None):
    # This ensures that all samples are within a bin
    number_of_bins = int(np.ceil(np.ptp(x) / step_size))
    bins = np.linspace(np.min(x), np.min(x) + step_size*number_of_bins,
                       num=number_of_bins+1)
    bins -= (bins[-1] - np.max(x)) / 2
    bin_centers = bins[:-steps_per_bin] + step_size*steps_per_bin/2

    counts, _ = np.histogram(x, bins=bins)
    vals, _ = np.histogram(x, bins=bins, weights=y)
    bin_avgs = vals / counts
    n = len(bin_avgs)
    windowed_bin_avgs = as_strided(bin_avgs,
                                   (n-steps_per_bin+1, steps_per_bin),
                                   bin_avgs.strides*2)

    weighted_average = np.average(windowed_bin_avgs, axis=1, weights=weights)

    return bin_centers, weighted_average

You can now do something like this:

#plot the moving average with triangular weights
weights = np.concatenate((np.arange(0, 5), np.arange(0, 5)[::-1]))
bins, average = moving_weighted_average(x, y, steps_per_bin=len(weights),
                                        weights=weights)
plt.plot(bins, average,label='moving average')

plt.show()

enter image description here

like image 22
Jaime Avatar answered Oct 22 '22 19:10

Jaime