Autocorrelation analysis in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Autocorrelation

What does a high positive autocorrelation at lag 1 indicate in a time series?

A Values at time t are negatively related to values at time t-1

B Values at time t are completely independent from values at time t-1

C Values at time t are strongly similar to values at time t-1

D Values at time t are random and show no pattern

💡 Hint

Think about how values close in time relate to each other.

High positive autocorrelation at lag 1 means the value now is similar to the value one step before, showing a pattern or trend.

❓ Predict Output

intermediate

Output of Autocorrelation Calculation

What is the output of the following Python code calculating autocorrelation for lag 1?

ML Python

import numpy as np
from statsmodels.tsa.stattools import acf

data = np.array([1, 2, 3, 4, 5])
result = acf(data, nlags=1, fft=False)
print(round(result[1], 2))

A 0.8

B 1.0

C 0.5

D 0.0

💡 Hint

Autocorrelation at lag 0 is always 1. Check how values relate at lag 1.

The autocorrelation at lag 1 for this increasing sequence is 0.8 approximately, showing strong positive correlation.

❓ Model Choice

advanced

Choosing Model Based on Autocorrelation

You observe strong autocorrelation at multiple lags in your time series data. Which model is best suited to capture this pattern?

A Decision Tree Classifier

B Linear Regression without lag features

C K-Means Clustering

D ARIMA (AutoRegressive Integrated Moving Average)

💡 Hint

Look for models designed for time series with autocorrelation.

ARIMA models explicitly model autocorrelation through autoregressive and moving average terms, making them ideal for such data.

❓ Hyperparameter

advanced

Selecting Lag Parameter for Autocorrelation

When computing autocorrelation for a time series, what is the effect of increasing the maximum lag parameter?

A You analyze relationships between points farther apart in time

B You increase the speed of computation

C You reduce the number of data points used in the calculation

D You ignore short-term dependencies

💡 Hint

Think about what lag means in time series.

Increasing max lag lets you check autocorrelation between points separated by more time steps, revealing longer-term patterns.

🔧 Debug

expert

Debugging Autocorrelation Calculation Error

What error will this code raise when calculating autocorrelation on a constant time series?

ML Python

import numpy as np
from statsmodels.tsa.stattools import acf

data = np.array([5, 5, 5, 5, 5])
result = acf(data, nlags=2, fft=False)
print(result)

A ZeroDivisionError: division by zero

B ValueError: The input data is constant

C TypeError: unsupported operand type(s)

D No error, outputs array of ones

💡 Hint

Consider variance of constant data in autocorrelation formula.

Autocorrelation calculation divides by variance. Constant data has zero variance causing division by zero error.

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