Classical cattle-cycle theory was developed mainly in temperate, capital-intensive livestock systems, leaving its external validity under tropical, extensive production conditions less well established. Using 851 monthly slaughter observations from Colombia (1954–2024), this study integrates seasonal ARIMA and spectral methods, Bai-Perron break tests, a five-variable VAR, external-shock ARIMAX tests, and a census-anchored Kalman reconstruction of herd inventory. The Christiano-Fitzgerald component yields an average complete-cycle duration of approximately 6.1 years, while multitaper evidence is multimodal, with concentrations around 4.4–5.0 and 7.1–7.8 years. Under the reference Bai-Perron specification, BIC selects seven breaks defining eight regimes; the first four dates are stable across nearby specifications, whereas later dates are more sensitive. Slaughter's own component explains 63.6–65.2% of its 24-month forecast-error variance across alternative Cholesky orderings. Conventional VAR Granger results do not survive Toda-Yamamoto robustness tests, and climate, interest rates, and the real exchange rate add no robust predictive content. The reconstructed herd shows a marked 2011–2019 contraction followed by recovery through 2024, although its magnitude is calibration-sensitive. The results extend evidence on retention-liquidation dynamics to a tropical, extensive, dual-purpose system while showing that individual channels remain context-dependent.