Hidden Markov Models (HMMs) are statistical models that assume a system is governed by hidden states, which can only be inferred through observed outputs. In an HMM, the system transitions between these hidden states at certain probabilities, and each state produces observable events or outputs, also at defined probabilities. This structure allows HMMs to model sequences where the underlying process is not directly observable, which is especially common in time series data. The key components of an HMM include the set of hidden states, the transition probabilities between these states, and the observation probabilities for the events produced by each state.
In time series applications, HMMs are particularly useful for tasks such as speech recognition, stock price prediction, and even biological sequence analysis. For instance, in speech recognition, the hidden states could represent different phonemes or sounds. As a person speaks, the model transitions through these states while generating audio signals (the observable outputs). By analyzing the sequence of sounds produced, an HMM can be used to identify the sequence of states that most likely generated the observed audio, leading to a transcription of the spoken words.
To implement an HMM in a time series context, developers often utilize algorithms like the Viterbi algorithm for decoding the most likely sequence of hidden states and the Baum-Welch algorithm for training the model parameters based on observed data. Libraries such as HMMlearn in Python provide tools for developers to create and work with HMMs efficiently. By applying HMMs, professionals can gain insights into temporal patterns and dependencies that are not immediately visible in the raw data, enabling more informed decision-making and predictive capabilities.