Time series evaluation metrics in ML Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Mean Absolute Error (MAE) in time series evaluation?

MAE measures the average absolute difference between predicted and actual values. It shows how far predictions are from true values on average, using simple absolute differences.

beginner

Explain Mean Squared Error (MSE) and why it is used.

MSE calculates the average of squared differences between predicted and actual values. Squaring emphasizes larger errors, making MSE sensitive to big mistakes.

beginner

What does Root Mean Squared Error (RMSE) represent?

RMSE is the square root of MSE. It gives error in the same units as the data, making it easier to understand how far predictions are from actual values.

intermediate

Describe Mean Absolute Percentage Error (MAPE) and its limitation.

MAPE shows average absolute error as a percentage of actual values. It is easy to interpret but can be misleading if actual values are near zero, causing very high or undefined percentages.

intermediate

Why is R-squared (Coefficient of Determination) used in time series evaluation?

R-squared measures how well the model explains the variation in the data. A value close to 1 means predictions fit the data well, while values near 0 mean poor fit.

Which metric gives error in the same units as the original data?

A Mean Squared Error (MSE)

B Root Mean Squared Error (RMSE)

C Mean Absolute Error (MAE)

D Mean Absolute Percentage Error (MAPE)

RMSE is the square root of MSE, so it has the same units as the original data, making it easier to interpret.

Which metric can be misleading when actual values are close to zero?

A MAPE

B R-squared

C RMSE

D MAE

MAPE divides by actual values, so when actual values are near zero, it can produce very large or undefined percentages.

What does a high R-squared value indicate in time series evaluation?

A Overfitting

B Poor model fit

C High error

D Good model fit

A high R-squared means the model explains most of the variation in the data, indicating good fit.

Which metric penalizes larger errors more heavily?

A MAE

B MAPE

C MSE

D R-squared

MSE squares the errors, so larger errors have a bigger impact on the metric.

Which metric is best to use when you want an error measure easy to understand as a percentage?

A MAPE

B RMSE

C MAE

D MSE

MAPE expresses error as a percentage, making it easy to understand relative error size.

Describe the main differences between MAE, MSE, and RMSE for evaluating time series predictions.

Think about how each metric treats errors and their units.

Explain why MAPE can be problematic with certain time series data and when you might avoid using it.

Consider what happens when dividing by numbers close to zero.

Practice

1. Which metric measures the average absolute difference between predicted and actual values in time series forecasting?

easy

A. Mean Squared Error (MSE)

B. Mean Absolute Error (MAE)

C. Root Mean Squared Error (RMSE)

D. R-squared (Coefficient of Determination)

Solution

1. Step 1: Understand the definition of MAE

   MAE calculates the average of the absolute differences between predicted and actual values, showing average error size.

2. Step 2: Compare with other metrics

   MSE and RMSE square errors, while R-squared measures variance explained, not average error.

3. Final Answer:

   Mean Absolute Error (MAE) -> Option B

4. Quick Check:

   Average absolute difference = MAE [OK]

Hint: MAE uses absolute differences, no squaring involved [OK]

Common Mistakes:

• Confusing MAE with MSE or RMSE
• Thinking R-squared measures error size
• Assuming RMSE is the same as MAE

2. Which of the following is the correct formula for Root Mean Squared Error (RMSE) given errors \(e_i = y_i - \hat{y}_i\) for \(n\) points?

easy

A. RMSE = \(\sum_{i=1}^n e_i^2\)

B. RMSE = \(\frac{1}{n} \sum_{i=1}^n |e_i|\)

C. RMSE = \(\frac{1}{n} \sum_{i=1}^n e_i\)

D. RMSE = \(\sqrt{\frac{1}{n} \sum_{i=1}^n e_i^2}\)

Solution

1. Step 1: Recall RMSE formula

   RMSE is the square root of the average of squared errors, so it must include squaring, averaging, then square root.

2. Step 2: Check each option

   RMSE = \(\sqrt{\frac{1}{n} \sum_{i=1}^n e_i^2}\): \(\sqrt{\frac{1}{n} \sum_{i=1}^n e_i^2}\) matches the formula exactly. RMSE = \(\sum_{i=1}^n e_i^2\) misses averaging and root. RMSE = \(\frac{1}{n} \sum_{i=1}^n |e_i|\) is MAE. RMSE = \(\frac{1}{n} \sum_{i=1}^n e_i\) is mean error (not squared).

3. Final Answer:

   RMSE = \(\sqrt{\frac{1}{n} \sum_{i=1}^n e_i^2}\) -> Option D

4. Quick Check:

   RMSE = sqrt(mean squared errors) [OK]

Hint: RMSE = square root of average squared errors [OK]

Common Mistakes:

• Forgetting to take square root
• Using absolute errors instead of squared
• Not dividing by number of points

3. Given actual values \([3, 5, 2, 7]\) and predicted values \([2, 5, 4, 8]\), what is the Mean Squared Error (MSE)?

medium

A. 1.5

B. 1.25

C. 2.0

D. 0.75

Solution

1. Step 1: Calculate errors and square them

   Errors: 3-2=1, 5-5=0, 2-4=-2, 7-8=-1. Squared errors: 1, 0, 4, 1.

2. Step 2: Compute average of squared errors

   Sum = 1+0+4+1=6. Average = 6/4 = 1.5.

3. Final Answer:

   1.5 -> Option A

4. Quick Check:

   Sum squared errors / count = 1.5 [OK]

Hint: Square errors, sum, then divide by count [OK]

Common Mistakes:

• Using absolute errors instead of squared
• Forgetting to average over all points
• Mixing predicted and actual values

4. Identify the error in this Python code calculating MAE for time series predictions:

def mae(actual, predicted):
    errors = [a - p for a, p in zip(actual, predicted)]
    return sum(errors) / len(errors)

medium

A. Use multiplication instead of subtraction in errors

B. Divide by sum of errors instead of length

C. Errors should be absolute values before summing

D. No error, code is correct

Solution

1. Step 1: Analyze error calculation

   The code calculates errors as differences but does not take absolute values, which MAE requires.

2. Step 2: Understand MAE definition

   MAE is mean of absolute errors, so errors must be wrapped with abs() before summing.

3. Final Answer:

   Errors should be absolute values before summing -> Option C

4. Quick Check:

   MAE needs absolute errors [OK]

Hint: MAE sums absolute errors, not raw differences [OK]

Common Mistakes:

• Skipping absolute value in error calculation
• Dividing by wrong denominator
• Confusing MAE with MSE

5. You have two forecasting models evaluated on the same dataset. Model A has MAE=2.5 and RMSE=3.0, Model B has MAE=2.0 and RMSE=3.5. Which model is generally better and why?

hard

A. Model A, because lower RMSE means fewer large errors

B. Model B, because higher RMSE indicates better fit

C. Model B, because lower MAE means better average error

D. Model A, because MAE and RMSE must be equal for best model

Solution

1. Step 1: Interpret MAE and RMSE values

   Model B has lower MAE but higher RMSE, meaning it has better average error but more large errors. Model A has lower RMSE, indicating fewer large errors.

2. Step 2: Decide which metric matters more

   RMSE penalizes large errors more, so lower RMSE often means more reliable predictions without big mistakes.

3. Final Answer:

   Model A, because lower RMSE means fewer large errors -> Option A

4. Quick Check:

   Lower RMSE means fewer big errors [OK]

Hint: Lower RMSE means fewer big errors; prefer it if large errors matter [OK]

Common Mistakes:

• Choosing model with lower MAE ignoring RMSE
• Thinking higher RMSE is better
• Expecting MAE and RMSE to be equal