Table 2 Filtering constraints for valid... | Emerald Publishing

Table 2

Filtering constraints for valid LPPLS window fits

Constraint	Condition	Interpretation
Power-law coefficient	−10 < B < − 10^–3	Ensures negative returns (downward pressure)
Oscillatory amplitude	0.01 < \|C\| < 1	Detects oscillatory structure, bounds magnitude
Log-price intercept	−100 < A < 100	Numerical stability for normalised log-prices
Minimum oscillations	$n_{osc} = \frac{ω}{2 π} \log \frac{t_{c} - t_{0}}{t_{c} - t_{1}} \geq 2.0$	Ensures log-periodic signature
Damping factor	$\frac{m \| B \|}{ω \| C \|} \geq 1$	Non-negative hazard rate (standard constraint)
Maximum relative error	rel_err ≤0.2	Model fit quality
Residual stationarity	ADF p < 0.05	White-noise residuals

Constraint	Condition	Interpretation
Power-law coefficient	−10 < B < − 10^–3	Ensures negative returns (downward pressure)
Oscillatory amplitude	0.01 < \|C\| < 1	Detects oscillatory structure, bounds magnitude
Log-price intercept	−100 < A < 100	Numerical stability for normalised log-prices
Minimum oscillations	$n_{osc} = \frac{ω}{2 π} \log \frac{t_{c} - t_{0}}{t_{c} - t_{1}} \geq 2.0$	Ensures log-periodic signature
Damping factor	$\frac{m \| B \|}{ω \| C \|} \geq 1$	Non-negative hazard rate (standard constraint)
Maximum relative error	rel_err ≤0.2	Model fit quality
Residual stationarity	ADF p < 0.05	White-noise residuals

Note(s): All seven conditions must be satisfied simultaneously for a window to contribute to indicator aggregation