Hidden Markov Models (HMMs) are probabilistic models used to represent systems that transition between hidden (unobservable) states over time, while producing observable outputs. At their core, HMMs assume that the system’s current state depends only on the previous state (the Markov property) and that each state generates an observable outcome based on a probability distribution. For example, in speech recognition, the hidden states could represent phonemes, and the observed outputs are audio signals. HMMs are defined by three components: transition probabilities (how states change over time), emission probabilities (how states produce observations), and initial state probabilities (starting conditions).
In time series analysis, HMMs are used to model sequences of data where underlying patterns or states evolve over time. A common application is predicting or classifying time-dependent data, such as stock prices, sensor readings, or biological sequences. For instance, an HMM could model weather patterns where hidden states represent “sunny” or “rainy” days, and observations are daily temperature readings. By training the model on historical data, developers can infer the most likely sequence of hidden states (e.g., predicting tomorrow’s weather) or calculate the probability of a new observation sequence (e.g., anomaly detection). Algorithms like the Viterbi algorithm (for finding the optimal state sequence) and the Forward-Backward algorithm (for estimating model parameters) are central to working with HMMs in practice.
Developers implement HMMs by defining the model structure, training it with data, and applying it to tasks like prediction or pattern recognition. For example, in financial forecasting, an HMM might track market regimes (e.g., “bull” or “bear” markets) based on stock volatility. The model is trained using historical price data to learn transition probabilities between regimes and emission probabilities linking regimes to observed metrics like trading volume. Once trained, the model can classify real-time data into hidden states or forecast future trends. Libraries like Python’s hmmlearn simplify implementation by providing tools for parameter estimation and inference. However, HMMs require careful tuning—such as choosing the number of hidden states or handling missing data—to avoid overfitting or inaccurate predictions. Despite limitations like the Markov assumption (ignoring long-term dependencies), HMMs remain a practical tool for time series problems with clear state-based dynamics.