White noise is the error process assumed in a time-series model when residual values show no meaningful correlation across time and maintain a stable variance. In an ARIMA model, the error term εt represents white noise, while sigma2 estimates the residual-error variance. section 7.3.10
Assess whether model residuals behave like white noise by checking:
- Residual plots for obvious patterns or trends. section 7.3.10
- Residual density for concentration around a mean of zero and approximate normality. section 7.3.10
- ACF and PACF plots for statistically significant correlations. section 7.3.10
Inspecting fitted-model residuals
Extract residuals with model_fit.resid[1:], then plot their values and kernel density using pandas and Matplotlib. A residual series with no visible pattern, a distribution centered near zero, and no significant ACF or PACF correlations supports the adequacy of the fitted ARIMA model. section 7.3.10
>>> residuals = model_fit.resid[1:] #1 >>> fig, ax = plt.subplots(1, 2) #2 >>> residuals.plot(title = \ >>> 'Residuals', ax = ax[0]) #3 >>> residuals.plot(title = \ >>> 'Density', >>> kind = 'kde', >>> ax = ax[1]) #4 >>> plt.tight_layout() #5 >>> plt.show() #6
Run the supplied plotting listing to inspect residual behavior and density after fitting a model. section 7.3.10
