How to Use EDA to Understand Distribution Shifts in Time Series Data

Understanding distribution shifts in time series data is crucial for building reliable models, especially when data behavior changes over time due to external factors or evolving patterns. Exploratory Data Analysis (EDA) plays a key role in detecting, diagnosing, and understanding these shifts to improve forecasting, anomaly detection, or decision-making systems.

What Are Distribution Shifts in Time Series Data?

Distribution shift refers to a change in the statistical properties of a dataset over time. In time series, it means that the underlying data distribution—such as mean, variance, or correlation structure—varies between different time periods. This can happen gradually or suddenly and affects model performance if not addressed.

Common types of distribution shifts in time series:

• Covariate Shift: The input features’ distribution changes over time.

• Prior Probability Shift: The distribution of the target variable changes.

• Concept Drift: The relationship between inputs and outputs evolves.

Why Detect Distribution Shifts?

Detecting distribution shifts early helps:

• Maintain model accuracy and reliability.

• Identify changes in the environment or system dynamics.

• Trigger model retraining or adaptation.

• Understand external factors influencing data changes.

Step-by-Step Guide to Using EDA to Understand Distribution Shifts

1. Visualize Time Series Data Over Different Periods

Start with visualizing your time series data split into different intervals. Common approaches:

• Plot the entire time series.

• Plot segments or windows (e.g., monthly, quarterly).

• Use rolling statistics (rolling mean, rolling variance).

Visual cues like changes in trend, seasonality, or volatility hint at potential shifts.

2. Summary Statistics Comparison

Calculate and compare summary statistics across different time windows:

• Mean, median

• Variance, standard deviation

• Skewness, kurtosis

Large differences across periods indicate distribution changes.

3. Histogram and Density Plots

Plot histograms or kernel density estimates (KDE) of the data for different time windows to compare distributions visually.

• Overlay distributions from different time intervals.

• Look for shifts in location, spread, or shape.

4. Use Statistical Tests for Distribution Comparison

Quantify differences using statistical hypothesis tests:

• Kolmogorov-Smirnov test: Compares two distributions to check if they differ significantly.

• Anderson-Darling test: Another goodness-of-fit test focusing on tail differences.

• Chi-square test: For categorical time series or binned continuous data.

• Permutation tests: For non-parametric comparison.

Run these tests between distributions from different time slices to confirm shifts.

5. Analyze Rolling Window Statistics

Compute statistics over rolling windows (e.g., 30-day rolling mean/variance) and plot over time to see trends in distribution changes.

• Detect gradual drifts or abrupt changes.

• Identify unstable periods.

6. Check Feature Correlations Over Time

For multivariate time series, investigate if relationships between variables change:

• Calculate correlation matrices over rolling windows.

• Visualize with heatmaps or line plots.

Shifts in correlation structures can indicate covariate or concept drift.

7. Visualize Time Series Decomposition Components

Decompose the series into trend, seasonality, and residuals using methods like STL (Seasonal-Trend decomposition using Loess).

• Examine if components change their behavior over time.

• Shifts in trend or seasonality point to distribution changes.

8. Use Dimensionality Reduction for Complex Time Series

Apply PCA or t-SNE on features extracted from time series windows to visualize clustering or shifts.

• Clusters appearing or disappearing over time indicate distribution changes.

9. Monitor Data Quality and Outliers

Check for changes in missing data patterns, spikes, or anomalies that may cause or indicate distribution shifts.

• Plot missing value heatmaps.

• Analyze outlier frequency over time.

10. Track Target Variable Distribution Changes (If Supervised)

In supervised tasks, plot and analyze changes in the target variable’s distribution and its relationship with features.

Tools and Libraries for EDA in Time Series

• Pandas/Matplotlib/Seaborn: For plotting and statistical summaries.

• Scipy/Statsmodels: For statistical tests and decomposition.

• TSFresh, Kats, River: Libraries specialized for time series feature extraction and drift detection.

• Scikit-learn: For PCA and other dimensionality reduction methods.

Example Workflow

Suppose you have daily sales data over 3 years and want to check if the distribution shifted in the last year:

1. Plot daily sales and rolling averages.

2. Compute mean and variance yearly.

3. Plot histograms for years 1, 2, and 3.

4. Run Kolmogorov-Smirnov tests comparing year 3 against years 1 and 2.

5. Decompose time series to check if seasonal patterns changed.

6. Calculate correlation between sales and marketing spend quarterly.

7. Detect anomalies and outliers across years.

If you find significant statistical differences and pattern changes, you have identified a distribution shift needing further investigation or model adjustment.

Using EDA to understand distribution shifts provides a data-driven foundation to manage temporal changes effectively, improving time series modeling robustness and insights.