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

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

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)

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

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])}

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 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.

Practice

1. What does autocorrelation measure in a time series dataset?

easy

A. The difference between the highest and lowest values in the data

B. The total sum of all data points in the series

C. The average value of the dataset

D. The relationship between current data points and past data points at different time lags

Solution

1. Step 1: Understand autocorrelation concept

   Autocorrelation checks how current values relate to past values at various time gaps (lags).

2. Step 2: Compare options to definition

   Only The relationship between current data points and past data points at different time lags correctly describes this relationship; others describe unrelated statistics.

3. Final Answer:

   The relationship between current data points and past data points at different time lags -> Option D

4. Quick Check:

   Autocorrelation = relationship with past points [OK]

Hint: Autocorrelation links current data to past data points [OK]

Common Mistakes:

• Confusing autocorrelation with average or sum
• Thinking it measures difference between max and min
• Assuming it only looks at immediate previous point

2. Which of the following Python code snippets correctly computes the autocorrelation at lag 1 for a list data?

easy

A. import numpy as np
np.corrcoef(data[:-1], data[1:])[0,1]

B. np.corrcoef(data, data)[0,1]

C. np.mean(data) - np.mean(data[1:])

D. np.sum(data) / len(data)

Solution

1. Step 1: Understand autocorrelation calculation

   Autocorrelation at lag 1 compares data points with the next point, so we correlate data[:-1] with data[1:].

2. Step 2: Check code correctness

   import numpy as np np.corrcoef(data[:-1], data[1:])[0,1] uses np.corrcoef correctly on shifted slices; others do not compute correlation at lag 1.

3. Final Answer:

   import numpy as np\nnp.corrcoef(data[:-1], data[1:])[0,1] -> Option A

4. Quick Check:

   Shifted slices correlation = import numpy as np np.corrcoef(data[:-1], data[1:])[0,1] [OK]

Hint: Use shifted slices for lag correlation in numpy [OK]

Common Mistakes:

• Using correlation of data with itself (option B)
• Calculating mean difference instead of correlation
• Using sum or mean instead of correlation

3. Given the time series data = [2, 4, 6, 8, 10], what is the autocorrelation at lag 1 using numpy's correlation coefficient?

medium

A. 0.9

B. 1.0

C. 0.8

D. 0.0

Solution

1. Step 1: Prepare shifted data slices

   data[:-1] = [2,4,6,8], data[1:] = [4,6,8,10]

2. Step 2: Calculate correlation coefficient

   These slices are perfectly linearly increasing, so correlation is 1.0.

3. Final Answer:

   1.0 -> Option B

4. Quick Check:

   Perfect linear increase = autocorrelation 1.0 [OK]

Hint: Perfect linear sequences have autocorrelation 1.0 [OK]

Common Mistakes:

• Calculating correlation with full data instead of shifted slices
• Confusing correlation with difference or ratio
• Rounding errors leading to wrong decimals

4. The following code attempts to compute autocorrelation at lag 2 but gives an error. What is the error?

import numpy as np
data = [1, 3, 5, 7, 9]
result = np.corrcoef(data[:-2], data[2:])[0,2]

medium

A. IndexError because index 2 is out of bounds for the correlation matrix

B. TypeError because data is a list, not a numpy array

C. ValueError because data slices have different lengths

D. No error, code runs correctly

Solution

1. Step 1: Analyze np.corrcoef output shape

   np.corrcoef returns a 2x2 matrix for two input arrays, so valid indices are 0 or 1.

2. Step 2: Check indexing in code

   Accessing [0,2] is invalid and causes IndexError.

3. Final Answer:

   IndexError because index 2 is out of bounds for the correlation matrix -> Option A

4. Quick Check:

   Correlation matrix max index = 1, so index 2 causes error [OK]

Hint: Correlation matrix for two arrays is 2x2, max index 1 [OK]

Common Mistakes:

• Assuming list input causes TypeError
• Thinking slices have different lengths (they are equal)
• Believing code runs without error

5. You have daily sales data showing a weekly pattern. How can autocorrelation analysis help you detect this seasonality?

hard

A. By plotting sales against time without any lag analysis

B. By calculating the average sales over the entire dataset

C. By computing autocorrelation at lag 7 to check if sales on a day relate to sales 7 days before

D. By computing autocorrelation only at lag 1

Solution

1. Step 1: Understand weekly seasonality

   Weekly seasonality means patterns repeat every 7 days.

2. Step 2: Use autocorrelation at lag 7

   Computing autocorrelation at lag 7 checks if sales today relate to sales 7 days ago, revealing weekly patterns.

3. Final Answer:

   By computing autocorrelation at lag 7 to check if sales on a day relate to sales 7 days before -> Option C

4. Quick Check:

   Weekly pattern detected by lag 7 autocorrelation [OK]

Hint: Match lag to season length to find repeating patterns [OK]

Common Mistakes:

• Using lag 1 only misses weekly pattern
• Ignoring lag and just averaging data
• Plotting without lag analysis misses seasonality