Regression analysis models relationships between variables — for example, how much a stock's return is explained by market returns, interest rates, or sector performance. Multiple regression can separate the contribution of each factor, helping isolate what truly drives returns.
Cointegration identifies pairs of securities that share a long-term equilibrium relationship, even if they diverge in the short term. This is the mathematical foundation of pairs trading and statistical arbitrage.
Monte Carlo simulation generates thousands of random scenarios to model uncertainty and estimate the probability distribution of portfolio outcomes. It helps answer questions like: What is the probability of losing more than 20% in a given year?
Machine learning methods — random forests, gradient boosting, neural networks — can identify non-linear patterns in financial data that traditional statistical methods miss. However, financial data is notoriously noisy, and ML models are prone to overfitting without careful validation.
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