Autocorrelation analysis in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the autocorrelation of a time series using numpy.

ML Python

import numpy as np

data = np.array([1, 2, 3, 4, 5])
mean = np.mean(data)
variance = np.var(data)

autocorr = np.correlate(data - mean, data - mean, mode=[1])[len(data)-1] / (variance * len(data))
print(autocorr)

Drag options to blanks, or click blank then click option'

A'full'

B'valid'

C'same'

D'none'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'valid' or 'same' mode which returns smaller arrays and misses some lags.

Not subtracting the mean before correlation.

The 'full' mode returns the complete autocorrelation sequence, which is needed to get the autocorrelation at lag 0.

2fill in blank

medium

Complete the code to compute the autocorrelation function for lags up to max_lag.

ML Python

def autocorrelation(data, max_lag):
    n = len(data)
    mean = sum(data) / n
    var = sum((x - mean) ** 2 for x in data) / n
    result = []
    for lag in range(max_lag + 1):
        cov = sum((data[i] - mean) * (data[i + lag] - mean) for i in range(n - lag)) / n
        result.append(cov / [1])
    return result

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An

Bmean

Cmax_lag

Dvar

Attempts:

3 left

💡 Hint

Common Mistakes

Dividing by mean or length instead of variance.

Not normalizing covariance, resulting in incorrect scale.

Autocorrelation at each lag is covariance divided by variance to normalize it between -1 and 1.

3fill in blank

hard

Fix the error in the code to correctly compute the autocorrelation using pandas.

ML Python

import pandas as pd

data = pd.Series([1, 2, 3, 4, 5])
autocorr_value = data.autocorr(lag=[1])
print(autocorr_value)

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A-1

B0

C1

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using lag=0 which returns 1 always.

Using lag greater than series length causing NaN.

The lag parameter specifies the number of periods to shift. Lag 1 means correlation with the previous value.

4fill in blank

hard

Fill both blanks to create a dictionary of autocorrelations for lags 0 to max_lag.

ML Python

def autocorr_dict(data, max_lag):
    return {lag: data.autocorr(lag=[1]) for lag in range([2])}

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Alag

Bmax_lag + 1

Cmax_lag

Dlag + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using fixed lag instead of loop variable.

Using range(max_lag) which excludes max_lag.

Use lag variable for autocorr lag and range up to max_lag + 1 to include max_lag.

5fill in blank

hard

Fill all three blanks to compute and plot the autocorrelation function using matplotlib.

ML Python

import matplotlib.pyplot as plt

def plot_autocorr(data, max_lag):
    autocorrs = [data.autocorr(lag=[1]) for lag in range([2])]
    plt.stem(range([3]), autocorrs, use_line_collection=True)
    plt.xlabel('Lag')
    plt.ylabel('Autocorrelation')
    plt.title('Autocorrelation Function')
    plt.show()

Drag options to blanks, or click blank then click option'

Alag

Bmax_lag + 1

Cmax_lag

Dlag + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using max_lag instead of max_lag + 1, missing last lag.

Using fixed lag instead of loop variable.

Use lag variable for autocorr lag, range up to max_lag + 1 to include max_lag, and same range for plotting.