Related papers: Long memory and multifractality: A joint test

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in…

Functional Magnetic Resonance Imaging~(fMRI) is widely used to study activation in the human brain. In most cases, data are commonly used to construct activation maps corresponding to a given paradigm. Results can be very variable, hence…

We study the problem of testing whether the missing values of a potentially high-dimensional dataset are Missing Completely at Random (MCAR). We relax the problem of testing MCAR to the problem of testing the compatibility of a collection…

In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses are generally very short, high-dimensional, and may have…

We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set.…

Despite their impressive performance on diverse tasks, large language models (LMs) still struggle with tasks requiring rich world knowledge, implying the limitations of relying solely on their parameters to encode a wealth of world…

Fine-tuning Large Language Models (LLMs) with multimodal encoders on modality-specific data expands the modalities that LLMs can handle, leading to the formation of Multimodal LLMs (MLLMs). However, this paradigm heavily relies on…

Deep neural networks are over-parameterized and easily overfit the datasets they train on. In the extreme case, it has been shown that these networks can memorize a training set with fully randomized labels. We propose using the curvature…

This article proposes omnibus portmanteau tests for contrasting adequacy of time series models. The test statistics are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the…

Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and…

We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range…

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…

Two formulations are proposed to filter out correlations in the residuals of the multivariate GARCH model. The first approach is to estimate the correlation matrix as a parameter and transform any joint distribution to have an arbitrary…

Memory emerges as the core module in the large language model (LLM)-based agents for long-horizon complex tasks (e.g., multi-turn dialogue, game playing, scientific discovery), where memory can enable knowledge accumulation, iterative…

Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact…

Despite their recent successes, Transformer-based large language models show surprising failure modes. A well-known example of such failure modes is their inability to length-generalize: solving problem instances at inference time that are…

Health economic evaluations based on patient-level data collected alongside clinical trials~(e.g. health related quality of life and resource use measures) are an important component of the process which informs resource allocation…

We introduce here for the first time the long-term swap rate, characterised as the fair rate of an overnight indexed swap with infinitely many exchanges. Furthermore we analyse the relationship between the long-term swap rate, the long-term…