quantwave_core/regimes/
hmm_gas.rs

1//! HMM-GAS (Score-Driven Transitions)
2//! 
3//! Source: Creal, Koopman, and Lucas (2013) 
4//! "Generalized Autoregressive Score Models with Applications."
5//! 
6//! HMM-GAS models allow transition probabilities to be time-varying, 
7//! driven by the scaled score of the observation likelihood.
8
9use crate::traits::Next;
10use crate::regimes::MarketRegime;
11use serde::{Deserialize, Serialize};
12
13/// A 2-state Hidden Markov Model with Score-Driven Transitions.
14#[derive(Debug, Clone, Serialize, Deserialize)]
15pub struct HMMGAS {
16    /// Parameters for p11 logit: [omega, alpha, phi]
17    pub p11_params: [f64; 3],
18    /// Parameters for p22 logit: [omega, alpha, phi]
19    pub p22_params: [f64; 3],
20    /// Latent logit states
21    f11: f64,
22    f22: f64,
23    pub means: [f64; 2],
24    pub stds: [f64; 2],
25    last_probs: [f64; 2],
26    initialized: bool,
27}
28
29impl HMMGAS {
30    pub fn new(
31        p11_params: [f64; 3],
32        p22_params: [f64; 3],
33        means: [f64; 2],
34        stds: [f64; 2],
35    ) -> Self {
36        Self {
37            p11_params,
38            p22_params,
39            f11: 2.0, // logit(0.88)
40            f22: 2.0,
41            means,
42            stds,
43            last_probs: [0.5, 0.5],
44            initialized: false,
45        }
46    }
47
48    fn logit_inv(f: f64) -> f64 {
49        1.0 / (1.0 + (-f).exp())
50    }
51
52    fn gaussian_pdf(x: f64, mu: f64, sigma: f64) -> f64 {
53        let variance = sigma * sigma;
54        let denom = (2.0 * std::f64::consts::PI * variance).sqrt();
55        let exponent = -((x - mu).powi(2)) / (2.0 * variance);
56        exponent.exp() / denom
57    }
58}
59
60impl Next<f64> for HMMGAS {
61    type Output = MarketRegime;
62
63    fn next(&mut self, x: f64) -> Self::Output {
64        // Current transition probabilities
65        let p11 = Self::logit_inv(self.f11);
66        let p22 = Self::logit_inv(self.f22);
67        
68        let a = [[p11, 1.0 - p11], [1.0 - p22, p22]];
69
70        let mut likelihoods = [0.0; 2];
71        let mut total_likelihood = 0.0;
72
73        // 1. Update Probabilities (Filtering)
74        for j in 0..2 {
75            let mut prob_j = 0.0;
76            for i in 0..2 {
77                prob_j += self.last_probs[i] * a[i][j];
78            }
79            let emission = Self::gaussian_pdf(x, self.means[j], self.stds[j]);
80            likelihoods[j] = prob_j * emission;
81            total_likelihood += likelihoods[j];
82        }
83
84        let next_probs = if total_likelihood > 0.0 {
85            [likelihoods[0] / total_likelihood, likelihoods[1] / total_likelihood]
86        } else {
87            self.last_probs
88        };
89
90        // 2. Score-Driven Update of Latent Transition States (Simplified GAS)
91        // In a full GAS model, we would use the scaled score of the log-likelihood.
92        // Here we use a simplified update based on the state probability shift.
93        let score11 = next_probs[0] - self.last_probs[0];
94        let score22 = next_probs[1] - self.last_probs[1];
95
96        self.f11 = self.p11_params[0] + self.p11_params[1] * score11 + self.p11_params[2] * self.f11;
97        self.f22 = self.p22_params[0] + self.p22_params[1] * score22 + self.p22_params[2] * self.f22;
98
99        self.last_probs = next_probs;
100        self.initialized = true;
101
102        if next_probs[0] > next_probs[1] {
103            MarketRegime::Steady
104        } else {
105            MarketRegime::Crisis
106        }
107    }
108}
quantwave_core/regimes/hmm_gas.rs

quantwave_core/regimes/
hmm_gas.rs
