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//! Hidden Markov Models (Hamilton 1989)
//!
//! Source: Hamilton, J. D. (1989).
//! "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle."
//! Econometrica, 57(2), 357-384.
//!
//! Implementation of a regime-switching Hidden Markov Model with Gaussian emissions.
//! Includes the Viterbi algorithm for online state decoding and placeholder for Baum-Welch training.
use crate::regimes::MarketRegime;
use crate::traits::Next;
use serde::{Deserialize, Serialize};
/// A Hidden Markov Model for regime detection.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HMM {
n_states: usize,
/// Transition probability matrix [from_state][to_state]
a: Vec<Vec<f64>>,
/// Emission means for each state
means: Vec<f64>,
/// Emission standard deviations for each state
stds: Vec<f64>,
/// Initial state probabilities
pi: Vec<f64>,
/// Last Viterbi log-probabilities for each state
last_delta: Vec<f64>,
initialized: bool,
}
impl HMM {
/// Creates a new HMM with pre-defined parameters.
pub fn new(a: Vec<Vec<f64>>, means: Vec<f64>, stds: Vec<f64>, pi: Vec<f64>) -> Self {
let n_states = a.len();
Self {
n_states,
a,
means,
stds,
pi,
last_delta: vec![0.0; n_states],
initialized: false,
}
}
/// Default 2-state HMM (Bull/Bear).
///
/// **Input contract: feed daily returns, not price.** The Gaussian emission
/// parameters below are hardcoded to the scale of daily fractional returns
/// (means near `0.001`/`-0.002`, stds near `0.01`/`0.02`). Feeding a raw price
/// series (e.g. `100.0`) makes `gaussian_pdf` underflow to `0.0` for *every*
/// state, which drives every `next()` call into a `-inf`/`-inf` tie that always
/// resolves to state `0` (Bull) — i.e. a silently constant output. The
/// `hmm_bull_bear` plugin wrapper (quantwave-py) calls [`Self::is_degenerate`]
/// after every [`Next::next`] to turn that case into an explicit error
/// instead of a silent wrong answer; callers driving the model directly
/// should do the same.
///
/// **State labels are `{1, 2}`, not `{0, 1}`** at the plugin/FFI boundary —
/// `0` is reserved for "no regime yet" (`MarketRegime::Steady`), Bull maps to
/// `1`, Bear to `2`. See `hmm_bull_bear` (quantwave-py) and `MarketRegime`.
pub fn bull_bear() -> Self {
Self::new(
vec![
vec![0.95, 0.05], // Bull -> Bull, Bull -> Bear
vec![0.10, 0.90], // Bear -> Bull, Bear -> Bear
],
vec![0.001, -0.002], // Daily returns: 0.1% for Bull, -0.2% for Bear
vec![0.01, 0.02], // Volatility: 1% for Bull, 2% for Bear
vec![0.5, 0.5],
)
}
/// Calculate Gaussian PDF: P(x | mu, sigma)
fn gaussian_pdf(x: f64, mu: f64, sigma: f64) -> f64 {
let variance = sigma * sigma;
let denom = (2.0 * std::f64::consts::PI * variance).sqrt();
let exponent = -((x - mu).powi(2)) / (2.0 * variance);
exponent.exp() / denom
}
/// Returns `true` when the most recent [`Next::next`] update produced a
/// `-inf` log-likelihood for *every* state, i.e. `gaussian_pdf` underflowed to
/// `0.0` for all states. This is the degenerate-input signature described on
/// [`Self::bull_bear`]: it means the observation is off the scale the
/// emission parameters were fit for (classically, raw price fed where daily
/// returns were expected), and `best_state` would otherwise silently stick at
/// index `0` forever. Callers that need to fail loudly instead of emitting a
/// constant regime should check this after every `next()` call.
pub fn is_degenerate(&self) -> bool {
self.initialized
&& self
.last_delta
.iter()
.all(|d| d.is_infinite() && d.is_sign_negative())
}
/// Normalized state probabilities from Viterbi log-deltas (for soft regime features).
pub fn state_probabilities(&self) -> Vec<f64> {
if !self.initialized {
return self.pi.clone();
}
let max_log = self
.last_delta
.iter()
.cloned()
.fold(f64::NEG_INFINITY, f64::max);
let mut probs: Vec<f64> = self
.last_delta
.iter()
.map(|&d| (d - max_log).exp())
.collect();
let sum: f64 = probs.iter().sum();
if sum > 0.0 {
for p in &mut probs {
*p /= sum;
}
}
probs
}
}
impl Next<f64> for HMM {
type Output = MarketRegime;
fn next(&mut self, x: f64) -> Self::Output {
let mut next_delta = vec![0.0; self.n_states];
let mut best_state = 0;
let mut max_prob = -f64::INFINITY;
if !self.initialized {
for i in 0..self.n_states {
let emission = Self::gaussian_pdf(x, self.means[i], self.stds[i]);
next_delta[i] = (self.pi[i] * emission).ln();
if next_delta[i] > max_prob {
max_prob = next_delta[i];
best_state = i;
}
}
self.initialized = true;
} else {
for j in 0..self.n_states {
let mut max_prev = -f64::INFINITY;
for i in 0..self.n_states {
// delta_j(t) = max_i [ delta_i(t-1) + ln(A_ij) ] + ln(P(x|j))
let prob = self.last_delta[i] + self.a[i][j].ln();
if prob > max_prev {
max_prev = prob;
}
}
let emission = Self::gaussian_pdf(x, self.means[j], self.stds[j]);
next_delta[j] = max_prev + emission.ln();
if next_delta[j] > max_prob {
max_prob = next_delta[j];
best_state = j;
}
}
}
self.last_delta = next_delta;
match best_state {
0 => MarketRegime::Bull,
1 => MarketRegime::Bear,
_ => MarketRegime::Cluster(best_state as u8),
}
}
}