Journal of Mathematical Techniques and Computational Mathematics(JMTCM)

University of Latvia, Rain, a bulvaris 19, R ¯ ¯iga, LV-1586, Latvia

Publications

• Research Article   
  The Clock of Regimes: Matrix-Analytic Solutions for Continuous-Time Survival in Discrete HMMs using the R KRONX Package*
  Author(s): Oscar Linares* and Ričards Bulavs
  
  Hidden Markov Models (HMMs) are widely used to identify latent regime dynamics in financial time series, yet standard R implementations report state membership probabilities rather than the structural geometry of residence and absorption (ruin). This paper introduces KRONX, an R package that extends discrete-time HMMs into a survival- analytic framework through a matrix-operator chain. Starting from a Student-t HMM transition matrix A, the package constructs a hazard-adjusted sub-stochastic operator Q, a sub-generator K = Q − I, and the fundamental matrix N = −K −1 of cumulative expected sojourn times before absorption—adapting the mean-residence-time machinery from compartmental analysis to financial regime dynamics. The core analytical contribution is an exact, closed-form derivation of residence weights and a finite-horizon ruin bound, avoiding the numerical.. Read More»
  

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