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.