Seasonality Detection in Time Series Data

Time series analysis is a core focus area of statistics and data science employed to detect and forecast patterns within sequential data. Through the analysis of points captured over time, analysts are able to identify trends, seasonal cycles and other time-varying relationships. Seasonal detection and management are critical in enhancing the integrity of time series data towards the training of models and forecasting.

Time series data

Time series data is a series of observations or measurements taken at successive, equally spaced points in time. Time series data is common in areas such as finance, economics, healthcare and climatology. In contrast to cross-sectional data, time series data offers information about how things change over time and enables the analysis of trends, seasonality and temporal relationships.

Seasonality

Seasonality in time series is recurring and regular patterns at a set interval, which is caused by weather, holidays or business cycles. Ice cream sales usually reach their peak during summer and decrease during winter. Seasonality can happen at any time interval, for instance, daily, weekly or yearly, and can have patterns such as increased weekend sales. Determining these regular patterns is necessary for precise time series forecasting

Why to Detect Seasonality in Time Series Data?

There are certain specific reasons that are discussed below:

• Pattern Detection: Identifying seasonality aids analysts in detecting repeating patterns, enhancing data interpretation and future prediction.
• Forecasting: Proper identification of seasonal trends assists in the development of stable forecasting models, resulting in better predictions.
• Anomaly Detection: Understanding the seasonal behavior of data allows us to spot anomalies that deviate from expected seasonal trends, signaling important events.
• Optimized Decision-Making: Recognizing seasonality allows organizations to optimize resources, adjust inventory and fine-tune strategies based on seasonal demands.

Handling Seasonality in Time Series Data

The easiest way to deal with seasonality is through seasonal differencing. Seasonal differencing eliminates the seasonal effect, thus converting the time series into stationary form, which is mostly necessary for forecasting accurately.

Seasonal differencing is achieved by taking away the data point from the same data point in the previous season. For instance, if you're dealing with monthly data and the seasonality recurs every 12 months, you would take away the current month's data from the data 12 months prior.

This process helps eliminate the cyclical patterns, making the data more suitable for model training. In Python, seasonal differencing can be easily applied using the .diff() method in Pandas, specifying a period (e.g., 12 for monthly data with yearly seasonality).

Step-by-step implementation

1. Importing required modules

To begin, we’ll import the necessary Python modules for data analysis, visualization and decomposition:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.tsa.seasonal import seasonal_decompose

2. Dataset loading and visualization

Next, we load a time-series dataset (e.g., US Airline Passengers) from Kaggle. We then visualize the original data to identify any patterns.

data = pd.read_csv('AirPassengers.csv')
data['Month'] = pd.to_datetime(data['Month'], format='%Y-%m')
data.set_index('Month', inplace=True)

# Plot the original time series data
plt.figure(figsize=(7, 5))
plt.plot(data, label='Original Time Series')
plt.title('Air Passengers Time Series')
plt.xlabel('Year')
plt.ylabel('Number of Passengers')
plt.legend()
plt.show()

Output

3. Data decomposition

Decompose the time series into trend, seasonal and residual components. We'll use a multiplicative model since the seasonal pattern is constant over different levels of the series.

# Decompose the time series into trend, seasonal and residual components
result = seasonal_decompose(
    data, model='multiplicative', extrapolate_trend='freq')
result.plot()
plt.suptitle('Seasonal Decomposition of Air Passengers Time Series')
plt.tight_layout()
plt.show()

Output

4. Visualizing the seasonality

Now we will visualize the only seasonal component by extracting it from the decomposition results.

# Plot the seasonal component
plt.figure(figsize=(6, 4))
plt.plot(result.seasonal, label='Seasonal Component')
plt.title('Seasonal Component of Air Passengers Time Series')
plt.xlabel('Year')
plt.ylabel('Seasonal Component')
plt.legend()
plt.show()

Output

5. Removing seasonality from the data

To use a time-series data for various purposes including model training it is required to have a seasonality free time-series data.

Equation:

d(t) = y(t) - y(t - m)

Where:

• d (t) is the differenced data point at time t.
• y (t) is the value of the series at time t.
• y (t - m) is the value of the data point at the previous season.
• m is the length of one season (in this case, m = 12 as we have yearly seasonality).

This equation represents seasonal differencing, used to remove the seasonal component from the data.

Here we will visualize how organized it will look after removing the seasonality.

# Plotting the original data and original data without the seasonal component
plt.figure(figsize=(7, 4))

# Plot the original time series data
plt.plot(data, label='Original Time Series', color='blue')
data_without_seasonal = data['#Passengers'] / result.seasonal

# Plot the original data without the seasonal component
plt.plot(data_without_seasonal,
         label='Original Data without Seasonal Component', color='green')
plt.title('Air Passengers Time Series with and without Seasonal Component')
plt.xlabel('Year')
plt.ylabel('Number of Passengers')
plt.legend()
plt.show()

Output

From the plot we can see that after removing seasonality the time-series data became very organized.

6. Applying the Augmented Dickey-Fuller (ADF) Test

Once we have eliminated the seasonality from our data, we have to test if the data series has turned stationary. One such method of testing stationarity is by applying the Augmented Dickey-Fuller (ADF) test. The ADF test is used to ascertain if a time series is stationary by conducting a test for the null hypothesis that the series contains a unit root (or is non-stationary).

Here’s how we can perform the ADF test:

from statsmodels.tsa.stattools import adfuller

#Perform the ADF test on the de - seasonalized data
    adf_result = adfuller(data_without_seasonal)

#Extract and display the test statistics and p - value
                     print('ADF Statistic:', adf_result[0]) print('p-value:', adf_result[1])

#Interpreting the results
                         if adf_result[1] < 0.05 : print("The data is stationary (p-value < 0.05).") else
    : print("The data is not stationary (p-value >= 0.05).")

Output

ADF Statistic: 1.1415289777074211 
p-value: 0.9955559262862962
The data is not stationary (p-value >= 0.05).

In this case, since the p-value is less than 0.05, we conclude that the data is stationary.

By applying the ADF test, we confirm that after removing the seasonal component from the time-series data, the data has become stationary. This step is crucial for ensuring that the time-series data is ready for further analysis or forecasting model training.

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