Post by Ibrahim Lanre

📊 Recently, I decided to explore the combination of Kalman Filters and Topological Data Analysis (TDA) based on the past articles i wrote about them TDA : https://lnkd.in/dCECQ2Q9 Kalman & particle filters : https://lnkd.in/dzriFcNq I started by applying a Kalman filter (local linear trend model) to both assets(SPY & GOLD) to extract innovations the part of price movement not explained by trend dynamics. From there, I moved into a more geometric perspective: 🔹 Persistent homology was computed on the 2D innovation space 🔹 H₀ captured clustering behavior (how tightly SPY and GLD move together) 🔹 H₁ revealed cyclic / mean-reverting structures 🔹 A rolling window tracked how these topological features evolved over time 🔹 Regimes were flagged when features exceeded mean + 2σ, signaling abnormal structural shifts in market behavior What I found interesting is how geometry and stochastic filtering can be combined to study market structure from a completely different angle. #QuantFinance #MachineLearning #StochasticProcesses #TopologicalDataAnalysis #KalmanFilter #SystematicTrading #FinancialEngineering Link to code: https://lnkd.in/ePsQUSc9

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