At1uri/multivariate-regime-switching-benchmarks

📊 Multivariate Markov Regime-Switching Microstructure Benchmark

An institutional econometric benchmark dataset curated by Ramprasad Atluri for training and benchmarking non-linear regime-switching models, hidden Markov models (HMMs), and state-dependent heteroskedastic volatility estimators.

📌 Theoretical Framework & Mathematical Formulation

Financial time series exhibit structural non-linearities, volatility clustering, and regime shifts that violate the traditional assumption of identically and independently distributed (i.i.d.) Gaussian increments.

This dataset implements a continuous discrete-time stochastic process governed by a latent $K=3$ state ergodic Markov chain $S_t \in {0, 1, 2}$:

$$y_t={\mu }_{S_t}+{\sigma }_{S_t}{ϵ}_t,{ϵ}_t\sim \text{i.i.d.}\mathcal{N}(0,1)y\_t\; =\; \backslash mu\_\{S\_t\}\; +\; \backslash sigma\_\{S\_t\}\; \backslash epsilon\_t,\; \backslash quad\; \backslash epsilon\_t\; \backslash sim\; \backslash text\{i.i.d.\}\; \backslash ,\; \backslash mathcal\{N\}(0,\; 1)$$

Latent State Definitions:

• State 0: Secular Low-Volatility Expansion ($\mu_0 = +0.0008, \sigma_0 = 0.008$)
• State 1: Mean-Reverting Equilibrium Consolidation ($\mu_1 = +0.0001, \sigma_1 = 0.014$)
• State 2: Turbulent Liquidity Cascade / High-Volatility Drawdown ($\mu_2 = -0.0018, \sigma_2 = 0.035$)

Transition Probability Kernel ($\mathbf{P}$):

The transition kernel $\mathbf{P} \in \mathbb{R}^{3 \times 3}$ defines the probability of transitioning from state $i$ to state $j$:

$$p_{ij}=\mathbb{P}(S_t=j\mid S_{t-1}=i)p\_\{ij\}\; =\; \backslash mathbb\{P\}(S\_t\; =\; j\; \backslash mid\; S\_\{t-1\}\; =\; i)$$

📐 Extreme-Value Volatility Estimators

Alongside standardized closing prices, this dataset provides continuous microstructural volatility estimators:

1. Parkinson Extreme-Value Volatility Estimator (1980): $$\sigma_{\text{Parkinson}} = \sqrt{\frac{1}{4 \ln 2} \ln\left(\frac{H_t}{L_t}\right)^2} \times \sqrt{252}$$

2. Garman-Klass Minimum-Variance Estimator (1980): $$\sigma_{\text{GK}} = \sqrt{0.5 \ln\left(\frac{H_t}{L_t}\right)^2 - (2 \ln 2 - 1) \ln\left(\frac{C_t}{O_t}\right)^2} \times \sqrt{252}$$

🚀 Loading in Python

import pandas as pd

url = "https://huggingface.co/datasets/At1uri/multivariate-regime-switching-benchmarks/raw/main/regime_switching_microstructure.csv"
df = pd.read_csv(url, parse_dates=["timestamp"])

print(df.info())
print(df.groupby("regime_label")[["log_return", "garman_klass_volatility"]].mean())

🛠️ Schema Definition

Feature	Type	Mathematical Meaning
timestamp	Date	Continuous trading day timestamp
close_price	Float	Asset valuation level $S_t$
log_return	Float	Continuously compounded return $r_t = \ln(S_t / S_{t-1})$
latent_regime	Integer	True latent Markov state $S_t \in {0, 1, 2}$
regime_label	String	Categorical regime descriptor
parkinson_volatility	Float	Annualized high-low volatility measure
garman_klass_volatility	Float	Minimum variance intraday jump-diffusion measure
prob_expansion	Float	Smoothed posterior probability $P(S_t = 0 \mid \mathcal{F}_T)$
prob_consolidation	Float	Smoothed posterior probability $P(S_t = 1 \mid \mathcal{F}_T)$
prob_turbulent	Float	Smoothed posterior probability $P(S_t = 2 \mid \mathcal{F}_T)$

⚖️ License

MIT License. Free for research, quantitative backtesting, and institutional modeling.