How to Visualize Time Series Forecasting Results with EDA

Visualizing time series forecasting results with Exploratory Data Analysis (EDA) helps you assess the model’s performance, spot patterns, and gain insights into trends, seasonality, and residuals. By using effective visualization techniques, you can ensure the forecasting model has captured the important data characteristics. Here’s how you can visualize your time series forecasting results with EDA:

1. Plotting the Actual vs Forecasted Values

• Objective: This basic visualization shows how closely your forecast matches the actual values over time.

• Method:

  • Use line plots to compare actual and predicted values. This allows you to visually assess whether your model tracks the fluctuations and trends of the actual data.

  • Highlight areas where the forecast underperforms or overperforms.

Example:

python
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import matplotlib.pyplot as plt
plt.figure(figsize=(10,6))
plt.plot(actual_values, label="Actual", color='blue')
plt.plot(forecasted_values, label="Forecast", color='red')
plt.title('Actual vs Forecasted Values')
plt.xlabel('Time')
plt.ylabel('Value')
plt.legend()
plt.show()

2. Residual Plots

• Objective: Residual plots (the difference between the forecast and actual values) help you evaluate the errors in your predictions.

• Method:

  • Plot the residuals to check if they exhibit randomness. Ideally, the residuals should be normally distributed with a mean close to zero and no discernible patterns (this means your model has captured the underlying patterns in the data).

  • If patterns are found in the residuals, it suggests that your model might have missed certain aspects of the data.

Example:

python
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residuals = actual_values - forecasted_values
plt.figure(figsize=(10,6))
plt.plot(residuals)
plt.title('Residual Plot')
plt.xlabel('Time')
plt.ylabel('Residuals')
plt.show()

3. Autocorrelation Plot (ACF and PACF)

• Objective: These plots help visualize if there are any significant correlations between residuals at different lags.

• Method:

  • Use the Autocorrelation Function (ACF) to plot the correlation of the residuals with their lagged values. High correlation at certain lags indicates a pattern that the model has not captured.

  • Use Partial Autocorrelation Function (PACF) to analyze how much of the autocorrelation is explained by previous lags.

Example:

python
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from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
plot_acf(residuals, lags=30)
plot_pacf(residuals, lags=30)
plt.show()

4. Rolling Mean and Rolling Standard Deviation

• Objective: Rolling statistics help you understand the trend and volatility over time. If the rolling mean is stable, it indicates a steady trend in the data.

• Method:

  • Plot the rolling mean and rolling standard deviation over time to inspect the trend and volatility.

  • If both of these statistics are constant over time, your data is likely stationary, which is an important assumption for many forecasting models.

Example:

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

plt.figure(figsize=(10,6))
plt.plot(actual_values, label="Actual")
plt.plot(rolling_mean, label="Rolling Mean", color='orange')
plt.plot(rolling_std, label="Rolling Std Dev", color='green')
plt.title('Rolling Mean and Standard Deviation')
plt.xlabel('Time')
plt.ylabel('Value')
plt.legend()
plt.show()

5. Seasonality Visualization

• Objective: Visualize any seasonality present in the data to determine whether the model effectively captures these seasonal patterns.

• Method:

  • Break down the time series data by year, month, or other relevant periods to plot the seasonal patterns.

  • Use box plots or heatmaps to observe how values change over specific time intervals.

Example:

python
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import seaborn as sns
data['Month'] = data['Date'].dt.month
sns.boxplot(x='Month', y='Value', data=data)
plt.title('Seasonality by Month')
plt.show()

6. Forecasting Error Distribution

• Objective: Understanding the distribution of forecasting errors (residuals) helps assess if the model is systematically biased.

• Method:

  • Plot a histogram or a kernel density estimate (KDE) of the residuals to check the distribution.

  • Ideally, the residuals should follow a normal distribution, suggesting that the model errors are random.

Example:

python
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import seaborn as sns
sns.histplot(residuals, kde=True)
plt.title('Residual Error Distribution')
plt.show()

7. Prediction Interval Plots

• Objective: Visualization of the forecast uncertainty using prediction intervals (upper and lower bounds around forecast).

• Method:

  • Plot the actual values, forecasted values, and the prediction intervals to see how well the model captures uncertainty.

  • Prediction intervals are particularly useful for assessing how the model performs in volatile periods.

Example:

python
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plt.figure(figsize=(10,6))
plt.plot(actual_values, label="Actual", color='blue')
plt.plot(forecasted_values, label="Forecast", color='red')
plt.fill_between(range(len(forecasted_values)),
                 lower_bound, upper_bound, color='grey', alpha=0.3)
plt.title('Forecast with Prediction Intervals')
plt.xlabel('Time')
plt.ylabel('Value')
plt.legend()
plt.show()

8. Cumulative Forecast Error Plot

• Objective: This plot helps assess the overall performance of the model by showing how the cumulative error evolves over time.

• Method:

  • Calculate the cumulative sum of residuals and plot it to detect any drift in the forecast.

Example:

python
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cumulative_residuals = residuals.cumsum()
plt.plot(cumulative_residuals)
plt.title('Cumulative Forecast Error')
plt.xlabel('Time')
plt.ylabel('Cumulative Residuals')
plt.show()

Conclusion

By using these visualizations, you can gain a deeper understanding of how well your forecasting model performs and where improvements might be needed. These plots help identify any issues with the model, like bias, seasonality, or unmodeled trends, and allow for better decision-making when refining forecasting models.