Related papers: Can Tests for Jumps be Viewed as Tests for Cluster…

In this paper, we address the challenge of clustering mixed-type data with temporal evolution by introducing the statistical jump model for mixed-type data. This novel framework incorporates regime persistence, enhancing interpretability…

Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation…

We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…

Many applications from the financial industry successfully leverage clustering algorithms to reveal meaningful patterns among a vast amount of unstructured financial data. However, these algorithms suffer from a lack of interpretability…

The data mining technique of time series clustering is well established in many fields. However, as an unsupervised learning method, it requires making choices that are nontrivially influenced by the nature of the data involved. The aim of…

We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…

Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous…

In this paper we consider two semimartingales driven by diffusions and jumps. We allow both for finite activity and for infinite activity jump components. Given discrete observations we disentangle the {\it integrated covariation} (the…

Clustered standard errors and approximate randomization tests are popular inference methods that allow for dependence within observations. However, they require researchers to know the cluster structure ex ante. We propose a procedure to…

In this paper, we propose a new threshold-kernel jump-detection method for jump-diffusion processes, which iteratively applies thresholding and kernel methods in an approximately optimal way to achieve improved finite-sample performance. We…

In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…

In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…

I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in…

Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for…

Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis,…

I introduce a simple permutation procedure to test conventional (non-sharp) hypotheses about the effect of a binary treatment in the presence of a finite number of large, heterogeneous clusters when the treatment effect is identified by…