Time series analysis patterns in Pandas - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of resampling time series data

What is the output of this code that resamples daily data to monthly sums?

Pandas

import pandas as pd

dates = pd.date_range('2023-01-01', periods=6, freq='D')
data = pd.Series([1, 2, 3, 4, 5, 6], index=dates)
result = data.resample('M').sum()
print(result)

A

2023-01-01    21
Freq: M, dtype: int64

B

2023-01-31    6
Freq: M, dtype: int64

C

2023-01-31    21
Freq: M, dtype: int64

D

2023-01-06    21
Freq: D, dtype: int64

💡 Hint

Monthly resampling sums all daily values in January.

The code sums all values from Jan 1 to Jan 6. Since the frequency is monthly ('M'), the result is indexed by the last day of January with the sum 1+2+3+4+5+6=21.

❓ data_output

intermediate

Number of missing values after forward fill

Given this time series with missing values, how many missing values remain after forward filling?

Pandas

import pandas as pd
import numpy as np

dates = pd.date_range('2023-01-01', periods=5, freq='D')
data = pd.Series([np.nan, 2, np.nan, 4, np.nan], index=dates)
filled = data.ffill()
missing_count = filled.isna().sum()
print(missing_count)

A 1

B 0

C 2

D 3

💡 Hint

Forward fill replaces NaN with previous non-NaN value. The first NaN has no previous value.

The first value is NaN and has no previous value to fill from, so it remains NaN. The other NaNs get filled. So 1 missing value remains.

❓ visualization

advanced

Identifying seasonality in time series plot

Which plot best shows clear seasonality in monthly sales data?

Pandas

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

np.random.seed(0)
dates = pd.date_range('2022-01-01', periods=24, freq='M')
sales = 10 + 5 * np.sin(2 * np.pi * dates.month / 12) + np.random.normal(0, 1, 24)
data = pd.Series(sales, index=dates)
plt.plot(data.index, data.values)
plt.title('Monthly Sales with Seasonality')
plt.xlabel('Date')
plt.ylabel('Sales')
plt.show()

A A histogram of sales values

B A scatter plot with random points and no pattern

C A bar chart with steadily increasing values

D A line plot showing repeating peaks every 12 months

💡 Hint

Seasonality means repeating patterns at regular intervals.

The line plot shows a smooth wave pattern repeating every 12 months, indicating seasonality.

🧠 Conceptual

advanced

Effect of differencing on time series data

What is the main effect of applying first-order differencing to a time series?

A It increases the variance of the series

B It removes trend and stabilizes the mean

C It smooths the series by averaging values

D It adds seasonality to the series

💡 Hint

Think about what subtracting consecutive values does to a trending series.

First-order differencing subtracts each value from the previous one, removing linear trends and making the mean more stable.

🔧 Debug

expert

Error raised by incorrect time series indexing

What error does this code raise when trying to access a time series value?

Pandas

import pandas as pd

dates = pd.date_range('2023-01-01', periods=3, freq='D')
data = pd.Series([10, 20, 30], index=dates)
value = data['2023-01-04']
print(value)

A KeyError

B IndexError

C TypeError

D ValueError

💡 Hint

Check if the date key exists in the index.

The date '2023-01-04' is not in the index, so accessing it raises a KeyError.

Practice

1. What is the main purpose of using a rolling average in time series analysis with pandas?

easy

A. To convert time series data into categorical data

B. To remove all missing values from the data

C. To smooth out short-term fluctuations and highlight longer-term trends

D. To sort the data by date in ascending order

Solution

1. Step 1: Understand rolling average concept

   A rolling average calculates the mean of data points in a moving window, smoothing short-term noise.

2. Step 2: Identify its effect on time series data

   This smoothing helps reveal longer-term trends by reducing random fluctuations.

3. Final Answer:

   To smooth out short-term fluctuations and highlight longer-term trends -> Option C

4. Quick Check:

   Rolling average = smoothing trends [OK]

Hint: Rolling average smooths data to show trends clearly [OK]

Common Mistakes:

• Thinking rolling average removes missing values
• Confusing rolling average with sorting
• Assuming it changes data type

2. Which of the following is the correct pandas syntax to calculate a 7-day rolling mean on a DataFrame column df['sales']?

easy

A. df['sales'].rolling(window=7).mean()

B. df['sales'].rolling(7).sum()

C. df.rolling(window=7)['sales'].sum()

D. df['sales'].rolling(window=7).median()

Solution

1. Step 1: Recall rolling syntax in pandas

   The rolling method is called on the Series with window=7 to specify 7 days.

2. Step 2: Apply mean function to get rolling average

   Using .mean() after rolling computes the rolling mean correctly.

3. Final Answer:

   df['sales'].rolling(window=7).mean() -> Option A

4. Quick Check:

   rolling(window=7).mean() = correct syntax [OK]

Hint: Use rolling(window=7).mean() for 7-day rolling average [OK]

Common Mistakes:

• Using rolling(7) without window= keyword
• Using sum() instead of mean() for average
• Applying rolling on DataFrame instead of Series

3. Given the following code, what will be the output of print(diff_series)?

import pandas as pd
s = pd.Series([10, 15, 20, 18, 25])
diff_series = s.diff()

medium

A. [NaN, 5.0, 5.0, -2.0, 7.0]

B. [10, 15, 20, 18, 25]

C. [NaN, 10, 15, 20, 18]

D. [5, 5, -2, 7, NaN]

Solution

1. Step 1: Understand what diff() does on a Series

   The diff() method calculates the difference between each element and its previous element.

2. Step 2: Calculate differences step-by-step

   Differences: NaN (no previous), 15-10=5, 20-15=5, 18-20=-2, 25-18=7.

3. Final Answer:

   [NaN, 5.0, 5.0, -2.0, 7.0] -> Option A

4. Quick Check:

   diff() = current - previous [OK]

Hint: diff() shows change from previous value [OK]

Common Mistakes:

• Forgetting first value is NaN
• Confusing diff() with cumulative sum
• Misordering differences

4. The following code throws an error. What is the cause?

import pandas as pd
dates = pd.date_range('2023-01-01', periods=5)
df = pd.DataFrame({'value': [1, 2, 3, 4, 5]}, index=dates)
rolling_sum = df.rolling(3).sum()
print(rolling_sum['value'])

medium

A. The rolling window size must be specified with window=3

B. There is no error; the code runs correctly

C. The rolling method cannot be used on DataFrames

D. The DataFrame index must be reset before rolling

Solution

1. Step 1: Check rolling syntax on DataFrame

   Using df.rolling(3).sum() is valid; window size can be passed as positional argument.

2. Step 2: Verify if code runs without error

   Rolling sum on DataFrame with datetime index works fine; no reset needed.

3. Final Answer:

   There is no error; the code runs correctly -> Option B

4. Quick Check:

   rolling(3) on DataFrame = valid [OK]

Hint: rolling() accepts window as positional argument [OK]

Common Mistakes:

• Assuming window= is mandatory
• Thinking index must be reset
• Believing rolling only works on Series

5. You have daily sales data in a DataFrame df with a datetime index. You want to detect if sales on a day are unusually high compared to the previous week. Which pandas method combination is best to identify these spikes?

hard

A. Sort the DataFrame by sales and pick top 7 days

B. Use diff() to find daily changes and select days with positive differences

C. Apply autocorrelation to find repeated patterns

D. Calculate 7-day rolling mean and then find days where sales exceed mean by a threshold

Solution

1. Step 1: Understand the goal to find spikes compared to previous week

   We want to compare each day's sales to the average of the last 7 days.

2. Step 2: Use rolling mean to get weekly average and compare

   Calculating 7-day rolling mean smooths data; days exceeding this mean by threshold indicate spikes.

3. Final Answer:

   Calculate 7-day rolling mean and then find days where sales exceed mean by a threshold -> Option D

4. Quick Check:

   Rolling mean + threshold = spike detection [OK]

Hint: Compare daily sales to 7-day rolling mean for spikes [OK]

Common Mistakes:

• Using diff() only finds changes, not spikes
• Sorting ignores time context
• Autocorrelation finds patterns, not spikes