How to Detect Seasonal Variations in Data Using EDA

Seasonal variations in data refer to patterns that repeat at regular intervals due to seasonal factors such as time of day, month, quarter, or year. Detecting these variations is crucial for understanding trends, making forecasts, and optimizing business strategies. Exploratory Data Analysis (EDA) offers effective techniques to uncover and visualize seasonal patterns before applying more complex models. This article explains how to detect seasonal variations in data using EDA, highlighting key methods and tools.

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Understanding Seasonal Variations

Seasonal variations are recurring fluctuations influenced by the calendar or natural cycles. For example, retail sales often peak during holidays, electricity usage rises during summer, and website traffic may vary by day of the week.

Characteristics of seasonal data:

• Regular intervals: Patterns repeat every fixed period (daily, weekly, monthly, quarterly, yearly).

• Predictable changes: The fluctuations are somewhat consistent in magnitude and timing.

• Non-random: Seasonality is systematic, unlike random noise.

Detecting these variations helps separate seasonality from overall trends and random noise in the data, improving forecasting accuracy.

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Step 1: Visualizing Time Series Data

Visual inspection is the first step in identifying seasonality.

• Line Plot: Plotting the time series data over the entire period helps spot repeating peaks and troughs.

  Example: Monthly sales data plotted over multiple years can reveal recurring spikes in certain months.

• Seasonal Subseries Plot: Break down data by season within each cycle (e.g., plotting each month across different years) to compare patterns.

• Lag Plot: Plotting the data against its lagged values (previous time points) can show periodic correlations indicative of seasonality.

Visualization tools such as matplotlib, seaborn, or plotly in Python are ideal for these plots.

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Step 2: Decomposition of Time Series

Decomposition splits data into three components: trend, seasonality, and residual (noise).

• Additive Model: When seasonal variations are constant over time.

  $$y_t = T_t + S_t + R_t$$

• Multiplicative Model: When seasonal effects change proportionally with the level of the time series.

  $$y_t = T_t times S_t times R_t$$

Using decomposition methods like STL (Seasonal-Trend decomposition using Loess) or classical decomposition can extract seasonal patterns visually and numerically.

Python libraries: statsmodels.tsa.seasonal.seasonal_decompose

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Step 3: Autocorrelation and Partial Autocorrelation Analysis

• Autocorrelation Function (ACF): Measures the correlation of the time series with its own lagged values. Peaks at specific lags indicate repeated patterns.

  For example, a peak at lag 12 in monthly data suggests yearly seasonality.

• Partial Autocorrelation Function (PACF): Helps understand the direct relationship between observations separated by a lag, controlling for intermediate lags.

Significant spikes at seasonal lags in ACF or PACF plots confirm the presence of seasonality.

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Step 4: Seasonal Subgroup Analysis

Divide data into groups based on seasons (e.g., months, quarters, days of the week) and analyze statistical properties.

• Boxplots by Season: Plotting boxplots for each month or quarter reveals distribution differences, highlighting seasonal effects.

• Mean or Median Comparison: Calculating average values per season shows systematic changes.

This method is useful to confirm visual observations and quantify seasonality.

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Step 5: Heatmaps and Calendar Plots

• Heatmaps: Display time series data in a matrix form where rows might represent years and columns months, with color intensity showing data magnitude. Seasonal patterns emerge as vertical stripes.

• Calendar Plots: Visualize daily or weekly data aligned to calendar dates to see how values change during specific times of the year.

These visualizations help uncover subtle seasonal variations and anomalies.

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Step 6: Statistical Tests for Seasonality

• Seasonal Mann-Kendall Test: Non-parametric test to detect seasonal trends.

• Friedman Test: Checks for differences between seasonal groups.

• Kruskal-Wallis Test: Useful when data does not follow normal distribution but seasonal groups need comparison.

These tests validate the significance of observed seasonality beyond visual intuition.

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Practical Example in Python

python
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import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import seasonal_decompose
from pandas.plotting import lag_plot
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
import seaborn as sns

# Load time series data
data = pd.read_csv('monthly_sales.csv', parse_dates=['Date'], index_col='Date')

# Line plot
data.plot(figsize=(12,6))
plt.title('Time Series Data')
plt.show()

# Seasonal decomposition
result = seasonal_decompose(data['Sales'], model='additive', period=12)
result.plot()
plt.show()

# Lag plot
lag_plot(data['Sales'])
plt.title('Lag Plot')
plt.show()

# ACF and PACF plots
plot_acf(data['Sales'], lags=40)
plt.show()
plot_pacf(data['Sales'], lags=40)
plt.show()

# Boxplot by month
data['Month'] = data.index.month
sns.boxplot(x='Month', y='Sales', data=data.reset_index())
plt.title('Monthly Sales Distribution')
plt.show()

# Heatmap
data_pivot = data.pivot_table(index=data.index.year, columns=data.index.month, values='Sales')
sns.heatmap(data_pivot, cmap='coolwarm')
plt.title('Heatmap of Monthly Sales')
plt.show()

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Conclusion

Detecting seasonal variations through EDA is an essential step in time series analysis. Visualization, decomposition, autocorrelation analysis, and seasonal subgrouping help reveal repeating patterns in data. Coupled with statistical tests, these methods provide a robust framework to identify seasonality, enabling better forecasting and strategic planning. Incorporating these techniques early in data analysis ensures seasonality is accurately understood and modeled.