How to Use EDA for Exploratory Time Series Forecasting

Exploratory Data Analysis (EDA) is a fundamental step in time series forecasting. It provides a deep understanding of data characteristics and uncovers hidden patterns, trends, seasonality, and anomalies that inform model selection and parameter tuning. Effective EDA ensures that models are both statistically sound and contextually appropriate. Here’s a comprehensive guide on how to use EDA for exploratory time series forecasting.

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Understanding the Time Series Structure

Time series data consist of observations collected sequentially over time. Each data point is timestamped and can be analyzed in terms of:

• Trend: Long-term increase or decrease in the data.

• Seasonality: Periodic fluctuations that repeat over a regular interval (e.g., hourly, daily, monthly).

• Cyclicality: Non-fixed periodic up and down movements, influenced by economic conditions or other external factors.

• Noise: Random variation that cannot be attributed to trend or seasonality.

Before delving into advanced models, understanding these components using EDA is essential.

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Step-by-Step EDA for Time Series Forecasting

1. Visual Inspection with Line Plots

Start by plotting the raw time series to gain a high-level understanding. A simple line graph reveals trends, seasonality, and sudden changes.

python
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import matplotlib.pyplot as plt
plt.plot(time_series)
plt.title("Time Series Plot")
plt.xlabel("Time")
plt.ylabel("Value")
plt.show()

Check for patterns over time and note any anomalies or changes in level or variance.

2. Decomposition of Time Series

Use decomposition to break the time series into trend, seasonality, and residual components.

python
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from statsmodels.tsa.seasonal import seasonal_decompose
result = seasonal_decompose(time_series, model='additive', period=12)
result.plot()
plt.show()

• Additive decomposition is used when seasonal variations are roughly constant.

• Multiplicative decomposition is used when seasonal variations increase over time.

3. Stationarity Testing

Stationarity is a key assumption in many time series models. A stationary series has a constant mean, variance, and autocorrelation over time. Use the Augmented Dickey-Fuller (ADF) test to check for stationarity.

python
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from statsmodels.tsa.stattools import adfuller
adf_result = adfuller(time_series)
print(f'ADF Statistic: {adf_result[0]}')
print(f'p-value: {adf_result[1]}')

A p-value less than 0.05 suggests the series is stationary. If not, apply transformations such as differencing, log, or Box-Cox.

4. Correlation and Lag Analysis

Understanding relationships between current and past values is crucial. Use autocorrelation (ACF) and partial autocorrelation (PACF) plots.

python
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from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
plot_acf(time_series)
plot_pacf(time_series)
plt.show()

• ACF reveals the degree of correlation between observations separated by various lags.

• PACF helps identify the direct effect of a lag after removing contributions from intervening lags.

5. Rolling Statistics

Analyze rolling mean and rolling standard deviation to check how these change over time, a visual way to confirm stationarity.

python
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rolling_mean = time_series.rolling(window=12).mean()
rolling_std = time_series.rolling(window=12).std()

plt.plot(time_series, label='Original')
plt.plot(rolling_mean, label='Rolling Mean')
plt.plot(rolling_std, label='Rolling Std')
plt.legend()
plt.show()

Significant changes over time in these metrics suggest non-stationarity.

6. Seasonal Plots

For strongly seasonal data, visualize seasonal effects using seasonal subseries plots or month-wise boxplots.

python
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import seaborn as sns
df['month'] = df.index.month
sns.boxplot(x='month', y='value', data=df)
plt.title("Seasonal Boxplot by Month")
plt.show()

These plots identify recurring patterns and provide insights into seasonality strength and variance.

7. Trend and Change Point Detection

Apply trend analysis to detect changes in direction and behavior.

• Use rolling averages for smoothing.

• Apply change point detection algorithms like PELT or BOCPD to locate structural breaks.

python
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import ruptures as rpt
model = "l2"
algo = rpt.Pelt(model=model).fit(time_series.values)
result = algo.predict(pen=10)
rpt.display(time_series.values, result)
plt.show()

Change points indicate where the statistical properties of the series change, such as shifts in mean or variance.

8. Time Series Transformation

Transformations like logarithms, square root, or Box-Cox stabilize variance and make patterns more visible.

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from scipy.stats import boxcox
transformed_data, lam = boxcox(time_series)

Use inverse transformations after forecasting to revert to the original scale.

9. Outlier Detection

Outliers distort forecasts. Use statistical tests or visualization to detect them:

• Z-score method for global outliers

• Moving average with thresholds

• Isolation Forest or Local Outlier Factor for more complex datasets

Visual inspection often helps:

python
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plt.plot(time_series)
plt.scatter(time_series.index[outlier_indices], time_series[outlier_indices], color='red')
plt.show()

10. Feature Engineering for Time Series

Create features that enhance model performance:

• Lag features: Past values (e.g., t-1, t-2)

• Rolling features: Moving average, max, min

• Datetime features: Day of week, month, quarter, holiday indicators

python
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df['lag1'] = df['value'].shift(1)
df['rolling_mean'] = df['value'].rolling(window=3).mean()
df['month'] = df.index.month

These engineered features are especially valuable in machine learning-based forecasting.

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Final Thoughts: Guiding Model Selection

By applying EDA techniques:

• Determine whether to use ARIMA, SARIMA, exponential smoothing, or machine learning models.

• Understand if differencing is necessary.

• Identify the nature and frequency of seasonality.

• Decide on feature sets for regression-based models.

• Spot any need for transformation or normalization.

EDA doesn’t just support accurate forecasting—it also improves interpretability, explains past behavior, and builds trust in the model’s predictions. Use it as a foundational tool before applying any sophisticated forecasting algorithms.