Time series components (trend, seasonality) in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Identifying trend in a time series

Which of the following best describes the trend component in a time series?

A Sudden spikes or drops caused by unexpected events

B Random fluctuations that do not follow any pattern

C A repeating pattern that occurs at regular intervals, like daily or yearly cycles

D A long-term increase or decrease in the data values over time

💡 Hint

Think about whether the data is generally going up or down over a long period.

The trend component shows the overall direction of the data over time, such as a steady rise or fall. Seasonality is about repeating cycles, and noise is random variation.

❓ Predict Output

intermediate

Output of seasonal decomposition

Given a time series with yearly seasonality and an upward trend, what will the seasonal component look like after decomposition?

ML Python

import numpy as np
import pandas as pd
from statsmodels.tsa.seasonal import seasonal_decompose

time = pd.date_range(start='2020-01-01', periods=24, freq='M')
data = 10 + 0.5 * np.arange(24) + 3 * np.sin(2 * np.pi * np.arange(24) / 12)
series = pd.Series(data, index=time)
result = seasonal_decompose(series, model='additive', period=12)
seasonal = result.seasonal.round(2).tolist()

A [0.0, 1.5, 3.0, 1.5, 0.0, -1.5, -3.0, -1.5, 0.0, 1.5, 3.0, 1.5, 0.0, 1.5, 3.0, 1.5, 0.0, -1.5, -3.0, -1.5, 0.0, 1.5, 3.0, 1.5]

B [10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5, 20.0, 20.5, 21.0, 21.5]

C [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

D [5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0, 15.5, 16.0, 16.5]

💡 Hint

Seasonal component repeats every 12 months and oscillates around zero.

The seasonal component captures the repeating yearly pattern, shown as a sine wave oscillating around zero. The trend is separate and increases steadily.

❓ Model Choice

advanced

Choosing a model for trend and seasonality

You have monthly sales data with a clear upward trend and yearly seasonal peaks. Which model is best to capture both components?

A ARIMA model without seasonal terms

B SARIMA model with seasonal order set to 12 months

C Simple Linear Regression on time index only

D K-Means clustering on sales values

💡 Hint

Consider models that explicitly handle seasonality.

SARIMA models include seasonal terms to capture repeating patterns like yearly seasonality, plus trend components. ARIMA without seasonality misses seasonal cycles.

❓ Hyperparameter

advanced

Selecting period parameter in seasonal decomposition

When using seasonal_decompose on daily data with weekly seasonality, what should the period parameter be set to?

A 365

B 30

C 7

D 12

💡 Hint

Think about how many days make a week.

The period parameter defines the length of one seasonal cycle. For weekly seasonality in daily data, the cycle length is 7 days.

❓ Metrics

expert

Evaluating model fit on decomposed components

After decomposing a time series into trend, seasonal, and residual components, which metric best measures how well the trend component fits the original data's long-term movement?

A Mean Absolute Error (MAE) between original series and trend component

B Root Mean Squared Error (RMSE) between seasonal component and original series

C R-squared value between residual component and original series

D Accuracy score comparing predicted and actual seasonal peaks

💡 Hint

Focus on measuring difference between trend and original data ignoring seasonality and noise.

MAE between original and trend shows how close the trend captures the long-term pattern. RMSE on seasonal or R-squared on residuals do not measure trend fit.