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A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
The increasing adoption of Digital Assets (DAs), such as Bitcoin (BTC), rises the need for accurate option pricing models. Yet, existing methodologies fail to cope with the volatile nature of the emerging DAs. Many models have been proposed…
Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…
With today's abundant streams of data, the only constant we can rely on is change. For stream classification algorithms, it is necessary to adapt to concept drift. This can be achieved by monitoring the model error, and triggering counter…
Time series often contain outliers and level shifts or structural changes. These unexpected events are of the utmost importance in fraud detection, as they may pinpoint suspicious transactions. The presence of such unusual events can easily…
In this work, we propose a model for estimating volatility from financial time series, extending the non-Gaussian family of space-state models with exact marginal likelihood proposed by Gamerman, Santos and Franco (2013). On the literature…
Predicting the intraday stock jumps is a significant but challenging problem in finance. Due to the instantaneity and imperceptibility characteristics of intraday stock jumps, relevant studies on their predictability remain limited. This…
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset…
This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including…
This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The state trajectory under stochastic jump process becomes random variables, which brings forth the probability distributions in the system…
In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the…
We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a…
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a…
Many methods for estimating integrated volatility and related functionals of semimartingales in the presence of jumps require specification of tuning parameters for their use in practice. In much of the available theory, tuning parameters…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…
This paper provides an analytical methodology to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) system. The hybrid ODE system is characterized by discontinuities…