**Residuals (Noise)
**This is the random “leftover” part of the data, the unpredictable ups and downs that can’t be explained by trend or seasonality.
Example: A one-time car purchase showing up in your monthly expense pattern.
Residuals may still show temporary patterns, such as a sales spike during a promotion or a sudden drop due to strikes or weather events.
Residual Analysis: How do you know if ARIMA is good model
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The residuals should approximate a Gaussian distribution (aka white noise).
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Visual inspection:
- ACF plot.: auto cor in residuals: expect no correlations
- Histogram.
- QQ plot. = - White noise should ideally follow a normal distribution.
- Statistical tests:
- Normality.
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&x2705; Histogram/Density plot.
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🤔 QQ-plot
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&x274C; Jarque-Bera (reliable for large sample size).
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&x274C; Shapiro-Wilk (reliable for large sample size).
- Autocorrelation.
- Heteroskedasticity.