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Hard · time_series · Quant Researcher interview question · ornstein_uhlenbeck, mean_reversion, maximum_likelihood, pairs_trading, time_series
The Ornstein-Uhlenbeck (OU) process is a continuous-time stochastic model used to describe mean-reverting dynamics in quantitative finance, such as interest rate spreads or statistical arbitrage residuals. Calibrating its parameters—mean-reversion speed θ, long-run mean μ, and volatility σ from discrete time-series data is a fundamental task. This is achieved by discretizing the process as an AR(1) model and using Ordinary Least Squares (OLS) for estimation. Task Implement the function ou_mle(s