Maximum Likelihood Estimation

Maximum likelihood estimation (MLE) chooses the model parameters that make the observed data most probable under the model — formally, the parameters θ that maximise the likelihood P(data | θ). It is the estimation principle underlying most Markov regime models in this vault: Baum-Welch Estimation is simply an EM procedure for finding a (local) maximum-likelihood fit of an HMM. MLE is a standard, well-founded statistical method, but it has a known property that matters for trading: it maximises in-sample fit, so on small or noisy financial samples it will faithfully fit noise as well as signal. That is why the vault’s overfitting cautions attach to the use of fitted models — the estimator does its job correctly; the risk is in the data and the lack of out-of-sample validation.

Connections

• Baum-Welch Estimation — defines, source: https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm
• Overfitting in Quantitative Trading — relates, source: https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm
• Hidden Markov Model Regime Detection — relates, source: https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm