Stationarity and differencing in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to difference the time series data once.

ML Python

differenced_series = original_series[1]

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

A.mean()

B.diff()

C.sum()

D.plot()

Attempts:

3 left

💡 Hint

Common Mistakes

Using .mean() instead of .diff()

Using .sum() which adds values rather than differencing

Trying to plot instead of transforming the data

The .diff() function calculates the difference between consecutive values, which helps to make a time series stationary.

2fill in blank

medium

Complete the code to check if the time series is stationary using the Augmented Dickey-Fuller test.

ML Python

from statsmodels.tsa.stattools import adfuller
result = adfuller(time_series)
print('p-value:', result[1])

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

A[1]

B[0]

C[4]

D[5]

Attempts:

3 left

💡 Hint

Common Mistakes

Using index 0 which is the test statistic, not p-value

Using index 4 or 5 which are not valid for p-value

The p-value is at index 1 in the result tuple returned by adfuller(). A low p-value indicates stationarity.

3fill in blank

hard

Fix the error in the code to difference the series twice.

ML Python

diff2_series = original_series[1].diff()

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

A.diff(1)

B.diff(2)

C.diff().diff()

D.diff()

Attempts:

3 left

💡 Hint

Common Mistakes

Using .diff(2) which is not the same as differencing twice

Using .diff(1) which only differences once

To difference twice, you apply diff() two times: .diff().diff(). Using diff(2) calculates the difference between values two steps apart, which is not the same.

4fill in blank

hard

Complete the code to difference the series once, drop NaNs, and print the p-value from the ADF test.

ML Python

differenced = original_series.diff()[1]
result = adfuller(differenced)
print('p-value:', result[2])

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

A.dropna()

B[1]

C[0]

D.values

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting .dropna(), causing errors in ADF test

Using [0] (test statistic) instead of [1] (p-value)

Differencing introduces NaN at the start, so chain .dropna() before running adfuller(). The p-value is result[1].

5fill in blank

hard

Fill all three blanks to extract the test statistic and p-value from the ADF test on differenced series, and reference critical values.

ML Python

adf_result = adfuller(differenced_series[1])
test_stat = adf_result[2]
p_value = adf_result[3]
critical_vals = adf_result[4]

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

A.dropna()

B[0]

C[1]

D[4]

Attempts:

3 left

💡 Hint

Common Mistakes

Omitting .dropna()

Mixing up indices (e.g., using [4] for p-value)

Using wrong tuple positions for stat and p-value

Remove NaNs with .dropna(). The ADF result tuple has test statistic at index [0], p-value at [1], and critical values dictionary at [4].

Practice

1. What does it mean when a time series is stationary?

easy

A. It has missing values that need to be filled

B. It has a clear upward or downward trend

C. It contains seasonal patterns repeating over fixed intervals

D. Its statistical properties like mean and variance do not change over time

Solution

1. Step 1: Understand stationarity definition

   Stationarity means the data's mean, variance, and other statistics stay constant over time.

2. Step 2: Compare options to definition

   Only Its statistical properties like mean and variance do not change over time describes constant statistical properties; others describe trends, seasonality, or missing data.

3. Final Answer:

   Its statistical properties like mean and variance do not change over time -> Option D

4. Quick Check:

   Stationary = constant mean/variance [OK]

Hint: Stationary means stats don't change over time [OK]

Common Mistakes:

• Confusing stationarity with trend presence
• Thinking seasonality means stationarity
• Assuming missing data affects stationarity

2. Which Python code correctly applies first-order differencing to a pandas Series data?

easy

A. data.dropna()

B. data.diff(1)

C. data.cumsum()

D. data.shift(1)

Solution

1. Step 1: Recall differencing method in pandas

   The diff(1) method calculates the difference between current and previous values, performing first-order differencing.

2. Step 2: Check other options

   shift(1) shifts data, cumsum() sums cumulatively, and dropna() removes missing values, none perform differencing.

3. Final Answer:

   data.diff(1) -> Option B

4. Quick Check:

   First difference = diff(1) [OK]

Hint: Use diff(1) for first-order differencing in pandas [OK]

Common Mistakes:

• Using shift instead of diff for differencing
• Confusing cumulative sum with differencing
• Dropping NaNs instead of differencing

3. Given this code snippet:

import pandas as pd
series = pd.Series([10, 12, 15, 20, 25])
diff_series = series.diff(1).dropna()
print(diff_series.tolist())

What is the output?

medium

A. [0, 2, 3, 5, 5]

B. [10, 12, 15, 20, 25]

C. [2.0, 3.0, 5.0, 5.0]

D. [nan, 2, 3, 5, 5]

Solution

1. Step 1: Calculate first differences

   Differences: 12-10=2, 15-12=3, 20-15=5, 25-20=5.

2. Step 2: Drop NaN and print list

   The first difference is NaN, dropped by dropna(), so output is [2.0, 3.0, 5.0, 5.0].

3. Final Answer:

   [2.0, 3.0, 5.0, 5.0] -> Option C

4. Quick Check:

   Diff values = [2.0,3.0,5.0,5.0] [OK]

Hint: First diff drops first NaN, output is differences list [OK]

Common Mistakes:

• Including NaN in output list
• Printing original series instead of differences
• Confusing shift with diff output

4. You applied first-order differencing to a time series but it still shows a trend. What is the likely issue?

medium

A. The series needs second-order differencing to remove the trend

B. You should use cumulative sum instead of differencing

C. The series is already stationary and differencing added noise

D. You forgot to normalize the data before differencing

Solution

1. Step 1: Understand differencing orders

   First-order differencing removes linear trends; if trend remains, higher order differencing may be needed.

2. Step 2: Evaluate other options

   Cumulative sum adds trend, normalization doesn't remove trend, and differencing adding noise means series was not stationary before.

3. Final Answer:

   The series needs second-order differencing to remove the trend -> Option A

4. Quick Check:

   Trend remains -> try second differencing [OK]

Hint: If trend remains, increase differencing order [OK]

Common Mistakes:

• Using cumulative sum instead of differencing
• Assuming normalization removes trend
• Stopping at first differencing without checking stationarity

5. You have a monthly sales time series with a yearly seasonal pattern and an upward trend. Which differencing approach should you apply to make it stationary?

hard

A. Apply first-order differencing followed by seasonal differencing with lag 12

B. Apply only first-order differencing

C. Apply only seasonal differencing with lag 12

D. Apply logarithm transformation without differencing

Solution

1. Step 1: Identify components to remove

   The series has both trend and yearly seasonality, so both need to be removed for stationarity.

2. Step 2: Choose differencing methods

   First-order differencing removes trend; seasonal differencing with lag 12 removes yearly seasonality.

3. Step 3: Combine differencing steps

   Applying first-order differencing then seasonal differencing is the correct approach to achieve stationarity.

4. Final Answer:

   Apply first-order differencing followed by seasonal differencing with lag 12 -> Option A

5. Quick Check:

   Trend + seasonality -> first + seasonal differencing [OK]

Hint: Remove trend then seasonality with two differencing steps [OK]

Common Mistakes:

• Applying only one differencing type ignoring trend or seasonality
• Using log transform alone to fix non-stationarity
• Confusing seasonal lag with differencing order