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Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…
Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical…
The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we…
Hidden Markov models (HMMs) and their extensions have proven to be powerful tools for classification of observations that stem from systems with temporal dependence as they take into account that observations close in time are likely…
We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit state transitions and makes for a robust…
This paper studies a fundamental problem regarding the security of blockchain on how the existence of multiple misbehaving pools influences the profitability of selfish mining. Each selfish miner maintains a private chain and makes it…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference…
This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and…
The regulatory framework of cryptocurrencies (and, in general, blockchain tokens) is of paramount importance. This framework drives nearly all key decisions in the respective business areas. In this work, a computational model is proposed…
In this paper, we prove that finite state space non parametric hidden Markov models are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly…
We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows…
In modern times, the cryptocurrency market is one of the world's most rapidly rising financial markets. The cryptocurrency market is regarded to be more volatile and illiquid than traditional markets such as equities, foreign exchange, and…
We search for digital biomarkers from Parkinson's Disease by observing approximate repetitive patterns matching hypothesized step and stride periodic cycles. These observations were modeled as a cycle of hidden states with randomness…
Crypto-coins (also known as cryptocurrencies) are tradable digital assets. Notable examples include Bitcoin, Ether and Litecoin. Ownerships of cryptocoins are registered on distributed ledgers (i.e., blockchains). Secure encryption…
When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the…
We study to what extent the Bitcoin blockchain security permanently depends on the underlying distribution of cryptocurrency market outcomes. We use daily blockchain and Bitcoin data for 2014-2019 and employ the ARDL approach. We test three…
In this paper, we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting. We first describe a more general model of…
Crypto enthusiasts claim that buying and holding crypto assets yields high returns, often citing Bitcoin's past performance to promote other tokens and fuel fear of missing out. However, understanding the real risk-return trade-off and what…
The main focus of this work is on developing models for the activity profile of a terrorist group, detecting sudden spurts and downfalls in this profile, and, in general, tracking it over a period of time. Toward this goal, a $d$-state…