Feat : hidden_markov_model

[MeKaustubh07]

Hidden Markov Model (HMM) – Quant Finance Overview

Purpose

Captures regime switching in financial markets — for example, transitions between bull and bear states.

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Key Idea

The market is treated as a latent state machine, where:

• Each hidden state represents a market regime
• Each state has its own probability distribution of returns
• The model learns transition probabilities between regimes

Mathematically:
[
P(S_t | S_{t-1}) = A_{ij}, \quad P(O_t | S_t) = B_j(O_t)
]
where

• ( S_t ): hidden state at time t
• ( O_t ): observed return at time t
• ( A_{ij} ): transition probability between states
• ( B_j ): emission probability for observations

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Use Cases

• Detecting market regimes
• Forecasting volatility states
• Generating algorithmic trading signals

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Minimal R Implementation

# Install dependencies
install.packages("depmixS4")

# Load library
library(depmixS4)

# Example: 2-state HMM on daily returns
set.seed(123)
returns <- diff(log(EuStockMarkets[, "DAX"]))  # sample data

# Build model
model <- depmix(response = returns ~ 1, 
                family = gaussian(), 
                nstates = 2, 
                data = data.frame(returns = returns))

# Fit model
fit_model <- fit(model)

# View results
summary(fit_model)

# Decode states (bull/bear)
states <- posterior(fit_model)
head(states)

[Copilot]

Pull Request Overview

Adds a new Hidden Markov Model (HMM) implementation for financial regime detection using an R6 class, including Baum–Welch (EM) training, Viterbi decoding, and helper utilities for regime labeling and summaries.

• Introduces HMM R6 class with fit, predict, posterior probability, and diagnostics.
• Includes example usage (guarded by if (FALSE)) for simulated data and basic signal generation.

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 5 comments.

[Copilot]

Pull Request Overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated 5 comments.