quantwave_core/regimes/
hsmm.rs

1//! Hidden Semi-Markov Models (HSMM)
2//! 
3//! Source: Yu (2010) "Hidden Semi-Markov Models"
4//! 
5//! HSMMs extend HMMs by allowing explicit modeling of the duration of each state, 
6//! avoiding the geometric duration distribution inherent in standard HMMs.
7
8use crate::traits::Next;
9use crate::regimes::MarketRegime;
10use serde::{Deserialize, Serialize};
11use statrs::distribution::{Discrete, Poisson};
12
13/// A distribution for the duration of a hidden state.
14#[derive(Debug, Clone, Serialize, Deserialize)]
15pub enum DurationDistribution {
16    /// Poisson distribution with mean lambda
17    Poisson { lambda: f64 },
18    /// Fixed duration
19    Fixed { duration: usize },
20}
21
22impl DurationDistribution {
23    pub fn p(&self, d: usize) -> f64 {
24        match self {
25            Self::Poisson { lambda } => {
26                let dist = Poisson::new(*lambda).unwrap();
27                dist.pmf(d as u64)
28            }
29            Self::Fixed { duration } => {
30                if d == *duration { 1.0 } else { 0.0 }
31            }
32        }
33    }
34}
35
36/// A Hidden Semi-Markov Model.
37#[derive(Debug, Clone, Serialize, Deserialize)]
38pub struct HSMM {
39    pub n_states: usize,
40    /// Transition matrix (diagonal must be zero)
41    pub a: Vec<Vec<f64>>,
42    pub means: Vec<f64>,
43    pub stds: Vec<f64>,
44    pub durations: Vec<DurationDistribution>,
45    /// Time spent in current state
46    current_duration: usize,
47    last_state: usize,
48    initialized: bool,
49}
50
51impl HSMM {
52    pub fn new(
53        a: Vec<Vec<f64>>,
54        means: Vec<f64>,
55        stds: Vec<f64>,
56        durations: Vec<DurationDistribution>,
57    ) -> Self {
58        Self {
59            n_states: a.len(),
60            a,
61            means,
62            stds,
63            durations,
64            current_duration: 0,
65            last_state: 0,
66            initialized: false,
67        }
68    }
69
70    fn gaussian_pdf(x: f64, mu: f64, sigma: f64) -> f64 {
71        let variance = sigma * sigma;
72        let denom = (2.0 * std::f64::consts::PI * variance).sqrt();
73        let exponent = -((x - mu).powi(2)) / (2.0 * variance);
74        exponent.exp() / denom
75    }
76}
77
78impl Next<f64> for HSMM {
79    type Output = MarketRegime;
80
81    fn next(&mut self, x: f64) -> Self::Output {
82        if !self.initialized {
83            self.initialized = true;
84            // Start in first state by default
85            return MarketRegime::Steady;
86        }
87
88        self.current_duration += 1;
89
90        // Calculate probability of staying vs switching
91        let prob_stay = self.durations[self.last_state].p(self.current_duration);
92        
93        let mut max_prob;
94        let mut best_state = self.last_state;
95
96        // 1. Evaluate staying in current state
97        let emission_stay = Self::gaussian_pdf(x, self.means[self.last_state], self.stds[self.last_state]);
98        max_prob = prob_stay * emission_stay;
99
100        // 2. Evaluate switching to other states
101        for j in 0..self.n_states {
102            if j == self.last_state { continue; }
103            
104            let transition_prob = self.a[self.last_state][j];
105            let emission_j = Self::gaussian_pdf(x, self.means[j], self.stds[j]);
106            // Probability of starting new state j (duration 1)
107            let prob_j = (1.0 - prob_stay) * transition_prob * self.durations[j].p(1) * emission_j;
108            
109            if prob_j > max_prob {
110                max_prob = prob_j;
111                best_state = j;
112            }
113        }
114
115        if best_state != self.last_state {
116            self.last_state = best_state;
117            self.current_duration = 1;
118        }
119
120        match best_state {
121            0 => MarketRegime::Steady,
122            1 => MarketRegime::Crisis,
123            _ => MarketRegime::Cluster(best_state as u8),
124        }
125    }
126}
quantwave_core/regimes/hsmm.rs

quantwave_core/regimes/
hsmm.rs
