How to Spot Seasonality and Trends in Time Series with EDA

Spotting seasonality and trends in time series data through Exploratory Data Analysis (EDA) is a crucial step in understanding the underlying patterns of the data, which can help in forecasting and making informed decisions. By leveraging various visualizations and statistical techniques, EDA helps uncover these patterns effectively. Below is an approach to spotting seasonality and trends in time series using EDA.

1. Visualizing the Time Series Data

One of the first and most intuitive methods to identify trends and seasonality is by visualizing the data. By plotting a time series graph, you can easily spot any long-term trends or periodic fluctuations that recur at regular intervals.

Steps:

• Plot the time series: This gives a direct visual representation of the data over time. The x-axis typically represents time, while the y-axis represents the value of the series.

• Look for upward or downward trends: An upward trend indicates that the data is increasing over time, while a downward trend suggests the opposite.

• Look for recurring patterns: If there are certain patterns that repeat after fixed intervals (daily, weekly, monthly, or yearly), it’s a sign of seasonality.

Example:

If you plot monthly sales data and see a clear peak every December, you might have identified seasonality due to the holiday shopping period.

2. Decompose the Time Series Data

Decomposition is another effective method to spot seasonality and trends. Time series decomposition separates the data into its constituent components: trend, seasonality, and residual (or noise). This can be done using statistical methods like classical decomposition or more advanced techniques like STL decomposition (Seasonal and Trend decomposition using LOESS).

Steps:

• Apply decomposition: You can decompose the series using statistical libraries in Python (like statsmodels or prophet) or R. The decomposition splits the time series into:

  • Trend: The long-term movement in the data.

  • Seasonality: The periodic fluctuations.

  • Residual: The noise or random variations.

Example:

Decomposing the time series will clearly highlight the trend (whether the series is moving upwards or downwards) and seasonality (whether there are repeating cycles).

3. Use Moving Averages

Moving averages help smooth out fluctuations in the data, making it easier to spot trends and seasonality.

Steps:

• Calculate moving averages: A moving average can be computed by averaging the values over a fixed window of time (e.g., 7-day, 30-day).

• Plot the moving average: By plotting the moving averages alongside the original time series, you can more easily see long-term trends and detect any cyclical or seasonal behavior.

Example:

If you apply a 12-month moving average to monthly sales data, a clear upward or downward trend will become evident, while seasonal fluctuations will be smoothed out.

4. Seasonal Subseries Plot

A seasonal subseries plot is useful for visualizing seasonality in time series data, especially when the data is grouped by season (like months or quarters).

Steps:

• Group the data by season: Split the time series data by season, such as by month or quarter.

• Plot each season: Each subseries can be plotted to compare the values for the same period across different years.

Example:

For monthly data, you can create subseries for each month of the year and compare the values for January across multiple years. This allows you to spot consistent seasonal patterns.

5. Autocorrelation and Partial Autocorrelation Plots

Autocorrelation plots show the correlation between the time series and its past values. By analyzing these plots, you can spot both trends and seasonality.

Steps:

• Plot the autocorrelation function (ACF): ACF helps identify the seasonality of the data by showing how the series is correlated with its previous values. If the series has a strong seasonal pattern, you will observe periodic spikes in the ACF plot.

• Plot the partial autocorrelation function (PACF): PACF helps in detecting the trend component of the data, especially for autoregressive models.

Example:

If there are spikes at lags of 12 months, 24 months, etc., this suggests the presence of yearly seasonality.

6. Check for Stationarity

Stationarity is an important concept in time series analysis. A stationary time series has constant mean, variance, and autocorrelation over time. If the time series is non-stationary, it likely contains a trend or seasonality.

Steps:

• Visual inspection: If the mean or variance of the time series changes over time, it’s likely non-stationary.

• Use statistical tests: The Augmented Dickey-Fuller (ADF) test can be used to formally test for stationarity. If the p-value is above 0.05, the series is non-stationary and likely contains trends or seasonality.

Example:

A non-stationary time series might show increasing values over time, indicating a trend. Applying a seasonal difference (subtracting a previous period’s value) might help in making the series stationary.

7. Use Fourier Transforms for Seasonality Detection

Fourier transforms help in detecting periodic components in time series data. By transforming the series into the frequency domain, you can identify dominant seasonal patterns.

Steps:

• Apply Fourier transform: Using tools like Fast Fourier Transform (FFT), you can decompose the time series into different frequency components.

• Identify peaks in the frequency domain: Peaks at specific frequencies indicate the presence of seasonality.

Example:

In a daily sales dataset, FFT might reveal that the data exhibits strong weekly cycles, showing seasonality.

8. Model Fitting and Residual Analysis

Fitting a time series model (e.g., ARIMA, Exponential Smoothing) to the data can help isolate the trend and seasonality. After fitting a model, you can analyze the residuals (the difference between the observed and predicted values) to check if any seasonality or trend remains.

Steps:

• Fit a model: Use models like ARIMA, SARIMA, or Exponential Smoothing to fit the time series.

• Analyze residuals: If the residuals display patterns or correlation, then there is likely remaining seasonality or trend in the data.

Example:

In a SARIMA model, the seasonal component (p, d, q) can directly indicate the seasonal behavior of the series.

Conclusion

Through these various EDA techniques—visualizations, decomposition, moving averages, autocorrelation, and residual analysis—you can effectively spot seasonality and trends in time series data. Understanding these patterns allows you to model the time series accurately and make more reliable forecasts. Identifying and separating out the trend and seasonal components also makes it easier to focus on the residuals (random noise) and improve the accuracy of predictive models.