Stationarity and differencing in ML Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean for a time series to be stationary?

A stationary time series has constant mean, constant variance, and constant autocovariance over time. This means its behavior does not change as time passes.

beginner

Why is stationarity important in time series analysis?

Many forecasting models assume stationarity because it makes patterns stable and predictable. Without stationarity, models may give unreliable predictions.

beginner

What is differencing in time series?

Differencing means subtracting the previous value from the current value to remove trends or seasonality, helping to make a time series stationary.

beginner

How do you perform first-order differencing on a time series?

First-order differencing subtracts each value by the value immediately before it: new_value = current_value - previous_value.

intermediate

What is the effect of over-differencing a time series?

Over-differencing can remove important information and add unnecessary noise, making the series harder to model and interpret.

Which of the following is NOT a characteristic of a stationary time series?

A Constant autocorrelation structure

B Constant variance over time

C Constant mean over time

D Increasing trend over time

A stationary time series does not have trends like increasing or decreasing patterns.

What is the main purpose of differencing a time series?

A To make the series stationary

B To add noise to the series

C To smooth the series

D To increase the series length

Differencing helps remove trends or seasonality to achieve stationarity.

How is first-order differencing calculated?

A Subtracting the previous value from the current value

B Adding the current and previous values

C Subtracting the current value from the next value

D Dividing the current value by the previous value

First-order differencing subtracts the previous value from the current value.

If a time series is already stationary, what happens if you apply differencing?

A It makes the series non-stationary

B It improves the model accuracy

C It may add unnecessary noise

D It has no effect

Differencing a stationary series can add noise and remove useful information.

Which test is commonly used to check stationarity?

A T-test

B Augmented Dickey-Fuller test

C Chi-square test

D ANOVA

The Augmented Dickey-Fuller test checks if a time series is stationary.

Explain in your own words what stationarity means and why it matters in time series forecasting.

Think about how a series that changes its behavior over time might confuse a forecasting model.

Describe how differencing helps to make a time series stationary and what risks come with over-differencing.

Consider differencing as a way to flatten the series but too much can harm it.

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