Time series components (trend, seasonality) in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to extract the trend component from a time series using moving average.

ML Python

trend = time_series.rolling(window=[1]).mean()

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

A12

B1

C3

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using window size 1 does not smooth the data.

Using window size 0 causes an error.

The moving average window size of 3 smooths short-term fluctuations to reveal the trend.

2fill in blank

medium

Complete the code to decompose a time series into trend, seasonality, and residual using statsmodels.

ML Python

from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(time_series, model=[1], period=12)

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

A"additive"

B"multiplicative"

C"linear"

D"exponential"

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'multiplicative' when seasonal effects are not proportional.

Using unsupported model types like 'linear'.

The 'additive' model assumes components add together: observed = trend + seasonality + residual.

3fill in blank

hard

Fix the error in the code to plot the seasonal component after decomposition.

ML Python

import matplotlib.pyplot as plt
result = seasonal_decompose(time_series, model="additive", period=12)
plt.plot(result.[1])
plt.show()

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

Aseasonal

Btrend

Cobserved

Dresidual

Attempts:

3 left

💡 Hint

Common Mistakes

Plotting trend or residual instead of seasonal component.

Using an attribute that does not exist.

The seasonal component is accessed with result.seasonal to plot seasonality.

4fill in blank

hard

Fill both blanks to create a dictionary of time series components with keys 'trend' and 'seasonality'.

ML Python

components = {"trend": result.[1], "seasonality": result.[2]

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

Atrend

Bseasonal

Cresidual

Dobserved

Attempts:

3 left

💡 Hint

Common Mistakes

Using residual or observed instead of trend or seasonal.

Mixing up keys and values.

The trend and seasonal components are accessed via result.trend and result.seasonal.

5fill in blank

hard

Fill all three blanks to compute the residual component by subtracting trend and seasonality from the original series.

ML Python

residual = time_series - result.[1] - result.[2]
print(residual.[3]())

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

Atrend

Bseasonal

Cdropna

Dfillna

Attempts:

3 left

💡 Hint

Common Mistakes

Using fillna() instead of dropna(), which fills missing values instead of removing them.

Mixing up trend and seasonal in subtraction.

Residual is original minus trend and seasonal. Use dropna() to remove missing values after subtraction.

Practice

1. Which component of a time series shows the long-term upward or downward movement over time?

easy

A. Trend

B. Seasonality

C. Noise

D. Residual

Solution

1. Step 1: Understand the meaning of trend

   The trend component represents the overall direction or pattern in the data over a long period, such as increasing sales over years.

2. Step 2: Differentiate from seasonality and noise

   Seasonality repeats in fixed cycles (like monthly), and noise is random variation. Trend is the smooth long-term movement.

3. Final Answer:

   Trend -> Option A

4. Quick Check:

   Long-term direction = Trend [OK]

Hint: Trend = overall direction over time, not repeating cycles [OK]

Common Mistakes:

• Confusing seasonality with trend
• Thinking noise is trend
• Mixing residual with trend

2. Which of the following is the correct Python code to plot seasonality in a time series using pandas?

easy

A. df['value'].plot()

B. df['value'].rolling(window=12).mean().plot()

C. df['value'].groupby(df.index.month).mean().plot()

D. df['value'].diff().plot()

Solution

1. Step 1: Identify how to extract seasonality

   Seasonality repeats in fixed intervals like months, so grouping by month and averaging shows seasonal pattern.

2. Step 2: Check code options

   df['value'].groupby(df.index.month).mean().plot() groups by month and plots mean, revealing seasonality. Others plot raw data, trend (rolling mean), or differences.

3. Final Answer:

   df['value'].groupby(df.index.month).mean().plot() -> Option C

4. Quick Check:

   Group by time period for seasonality plot [OK]

Hint: Group data by time unit (month) to see seasonality [OK]

Common Mistakes:

• Plotting raw data only
• Using rolling mean for seasonality
• Plotting differences instead of seasonal groups

3. Given this Python code snippet, what will be the output type of seasonal?

import pandas as pd
import numpy as np
index = pd.date_range('2023-01-01', periods=12, freq='M')
data = np.sin(np.linspace(0, 2 * np.pi, 12))
df = pd.Series(data, index=index)
seasonal = df.groupby(df.index.month).transform('mean')

medium

A. A numpy array of length 12

B. A pandas Series with same length as df

C. A pandas DataFrame with 12 rows and 1 column

D. A single float value representing mean

Solution

1. Step 1: Understand groupby with transform

   Using groupby with transform('mean') returns a Series aligned with original index, same length as df.

2. Step 2: Check output type

   Since df is a Series, seasonal is also a Series with same length, each value replaced by group mean.

3. Final Answer:

   A pandas Series with same length as df -> Option B

4. Quick Check:

   groupby + transform returns Series matching original length [OK]

Hint: groupby + transform keeps original length Series [OK]

Common Mistakes:

• Thinking transform returns single value
• Confusing transform with aggregate
• Expecting DataFrame instead of Series

4. You have this code to extract trend using rolling mean:

trend = df['value'].rolling(window=3).mean()

But the output has many NaN values at the start. How can you fix this?

medium

A. Use diff() instead of rolling mean

B. Change window to 1

C. Drop NaN values after rolling mean

D. Use min_periods=1 in rolling to reduce NaNs

Solution

1. Step 1: Understand rolling mean NaNs

   Rolling mean with window=3 needs 3 values to compute, so first 2 are NaN by default.

2. Step 2: Use min_periods to allow fewer values

   Setting min_periods=1 lets rolling mean compute with fewer points, reducing NaNs at start.

3. Final Answer:

   Use min_periods=1 in rolling to reduce NaNs -> Option D

4. Quick Check:

   min_periods controls minimum data points for rolling [OK]

Hint: Set min_periods=1 in rolling to avoid initial NaNs [OK]

Common Mistakes:

• Changing window to 1 loses smoothing
• Dropping NaNs loses early data
• Using diff() does not fix NaNs

5. You have monthly sales data with a strong yearly seasonality and an upward trend. Which method best separates trend and seasonality components?

hard

A. Use moving average with window=12 for trend, then subtract to get seasonality

B. Use differencing with lag=1 to remove seasonality

C. Apply Fourier transform to remove trend

D. Use rolling mean with window=3 to capture seasonality

Solution

1. Step 1: Understand yearly seasonality and trend

   Yearly seasonality repeats every 12 months; trend is slow upward movement.

2. Step 2: Choose method to separate components

   Moving average with window=12 smooths out seasonality, capturing trend. Subtracting trend leaves seasonality.

3. Step 3: Evaluate other options

   Differencing with lag=1 removes short-term changes, not yearly seasonality. Fourier transform is complex. Rolling mean with window=3 is too short for yearly seasonality.

4. Final Answer:

   Use moving average with window=12 for trend, then subtract to get seasonality -> Option A

5. Quick Check:

   Window matches season length to isolate trend [OK]

Hint: Match moving average window to season length to isolate trend [OK]

Common Mistakes:

• Using too short window for moving average
• Confusing differencing lag with season length
• Ignoring trend when extracting seasonality