Stationarity and differencing in ML Python - Model Pipeline Trace

Model Pipeline - Stationarity and differencing

This pipeline shows how we prepare time series data by checking if it is stationary and then use differencing to make it stationary. Stationary data means its patterns do not change over time, which helps models learn better.

Data Flow - 4 Stages

1Raw time series data

1000 time points x 1 feature→Collect original time series values→1000 time points x 1 feature

[100, 102, 105, 107, 110, ...]

↓

2Stationarity check

1000 time points x 1 feature→Perform Augmented Dickey-Fuller test to check stationarity→1000 time points x 1 feature + stationarity result

p-value=0.3 (non-stationary)

↓

3Differencing

1000 time points x 1 feature→Subtract previous value from current to remove trend→999 time points x 1 feature

[2, 3, 2, 3, ...] (differences of original series)

↓

4Stationarity re-check

999 time points x 1 feature→Perform Augmented Dickey-Fuller test again→999 time points x 1 feature + stationarity result

p-value=0.01 (stationary)

Training Trace - Epoch by Epoch

Loss
0.5 |****
0.4 |****
0.3 |****
0.2 |****
     1  2  3  4  5 Epochs

Epoch	Loss ↓	Accuracy ↑	Observation
1	0.45	0.60	Model starts learning with non-stationary data, loss is moderate.
2	0.38	0.68	Loss decreases as model adapts, accuracy improves.
3	0.30	0.75	Better learning after differencing, loss drops further.
4	0.25	0.80	Model converges well on stationary data.
5	0.22	0.83	Training stabilizes with low loss and high accuracy.

Prediction Trace - 4 Layers

Layer 1: Input raw time series value

Layer 2: Differencing operation

Layer 3: Model prediction on differenced data

Layer 4: Inverse differencing

Model Quiz - 3 Questions

Why do we perform differencing on time series data?

A To add noise to the data

B To increase the number of data points

C To make the data stationary by removing trends

D To change the data format to categorical

Key Insight

Making time series data stationary by differencing helps models learn patterns better, leading to lower loss and higher accuracy during training.

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