Resampling time series in Data Analysis Python - Time & Space Complexity

Time Complexity: Resampling time series

O(n)

Understanding Time Complexity

When working with time series data, resampling helps us change the frequency of data points.

We want to know how the time it takes to resample grows as the data size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import pandas as pd

dates = pd.date_range('2023-01-01', periods=1000, freq='T')
data = pd.Series(range(1000), index=dates)

resampled = data.resample('H').mean()

This code creates a time series with 1000 minute-level points and resamples it to hourly data by averaging.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Grouping data points by hour and computing the mean for each group.
• How many times: The number of groups depends on input size; roughly one group per hour in the data.

How Execution Grows With Input

As the number of data points grows, the number of groups grows proportionally, and each group's mean is computed.

Input Size (n)	Approx. Operations
10	About 1 group, 10 operations
100	About 1-2 groups, 100 operations
1000	About 16 groups, 1000 operations

Pattern observation: Operations grow roughly in direct proportion to the number of data points.

Final Time Complexity

Time Complexity: O(n)

This means the time to resample grows linearly as the number of data points increases.

Common Mistake

[X] Wrong: "Resampling time is constant no matter how much data there is."

[OK] Correct: More data means more groups and more calculations, so time grows with data size.

Interview Connect

Understanding how resampling scales helps you handle real-world time series data efficiently and shows you can think about performance.

Self-Check

"What if we resampled to a daily frequency instead of hourly? How would the time complexity change?"

Practice

1. What does resampling a time series data mean?

easy

A. Removing missing values

B. Sorting the data by values

C. Changing the time frequency of the data

D. Converting data to strings

Solution

1. Step 1: Understand the meaning of resampling

   Resampling means changing how often data points appear in time, like from daily to monthly.

2. Step 2: Compare options to definition

   Only Changing the time frequency of the data correctly describes changing the time frequency of data.

3. Final Answer:

   Changing the time frequency of the data -> Option C

4. Quick Check:

   Resampling = Changing frequency [OK]

Hint: Resampling changes how often data points appear [OK]

Common Mistakes:

• Thinking resampling sorts data
• Confusing resampling with cleaning data
• Believing resampling changes data type

2. Which of the following is the correct syntax to resample a pandas DataFrame df to monthly frequency and take the mean?

easy

A. df.resample('month').mean()

B. df.resample('monthly').mean()

C. df.resample('M').average()

D. df.resample('M').mean()

Solution

1. Step 1: Identify the correct frequency string

   Pandas uses 'M' for monthly frequency, not 'monthly' or 'month'.

2. Step 2: Check aggregation function name

   The correct function is mean(), not average().

3. Final Answer:

   df.resample('M').mean() -> Option D

4. Quick Check:

   Use 'M' and mean() for monthly average [OK]

Hint: Use 'M' for month and mean() to aggregate [OK]

Common Mistakes:

• Using 'monthly' or 'month' instead of 'M'
• Using average() instead of mean()
• Missing parentheses after mean

3. Given the following code, what will be the output?

import pandas as pd
idx = pd.date_range('2023-01-01', periods=4, freq='D')
data = [10, 20, 30, 40]
df = pd.DataFrame({'value': data}, index=idx)
resampled = df.resample('2D').sum()
print(resampled)

medium

A. 2023-01-01 30
2023-01-03 70

B. 2023-01-01 10
2023-01-03 30
2023-01-05 40

C. 2023-01-01 30
2023-01-03 40

D. 2023-01-01 10
2023-01-02 20
2023-01-03 30
2023-01-04 40

Solution

1. Step 1: Understand the original data and frequency

   Data has values 10,20,30,40 on consecutive days from 2023-01-01 to 2023-01-04.

2. Step 2: Resample with '2D' and sum

   Resampling groups every 2 days: (Jan 1+2) and (Jan 3+4). Sums are 10+20=30 and 30+40=70.

3. Final Answer:

   2023-01-01 30 2023-01-03 70 -> Option A

4. Quick Check:

   Sum every 2 days = 30, 70 [OK]

Hint: Sum values in 2-day groups starting from first date [OK]

Common Mistakes:

• Summing only one day instead of two
• Confusing sum with mean
• Misreading the date index

4. What is wrong with this code snippet?

df = pd.DataFrame({'value': [1, 2, 3]}, index=pd.date_range('2023-01-01', periods=3))
resampled = df.resample('W').mean

medium

A. Missing parentheses after 'mean' function call

B. Wrong frequency string 'W' for weekly resampling

C. DataFrame index is not a datetime index

D. Aggregation function 'mean' does not exist

Solution

1. Step 1: Check the resample syntax

   The code uses mean without parentheses, so it returns a method, not the result.

2. Step 2: Verify frequency and index

   'W' is correct for weekly, and the index is a datetime index, so no issues there.

3. Final Answer:

   Missing parentheses after 'mean' function call -> Option A

4. Quick Check:

   Call mean() with () to get result [OK]

Hint: Add () after mean to execute function [OK]

Common Mistakes:

• Forgetting parentheses on aggregation functions
• Thinking 'W' is invalid frequency
• Not setting datetime index before resampling

5. You have minute-level temperature data in a DataFrame df indexed by datetime. You want to resample it to hourly data but only keep hours where the average temperature is above 20°C. Which code snippet correctly does this?

hard

A. df.resample('H').mean()[lambda x: x['temperature'] > 20]

B. df.resample('H').mean().query('temperature > 20')

C. df.resample('H').mean()[df.resample('H').mean() > 20]

D. df.resample('H').mean().filter(lambda x: x > 20)

Solution

1. Step 1: Resample to hourly and calculate mean

   Use df.resample('H').mean() to get hourly averages.

2. Step 2: Filter rows where temperature > 20

   Using .query('temperature > 20') filters rows correctly by the 'temperature' column.

3. Final Answer:

   df.resample('H').mean().query('temperature > 20') -> Option B

4. Quick Check:

   Use query() to filter by column condition [OK]

Hint: Use query() after resample mean to filter rows [OK]

Common Mistakes:

• Applying boolean filter on DataFrame without column name
• Using filter() incorrectly for row filtering
• Repeating resample twice causing inefficiency