Related papers: Long memory and multifractality: A joint test
We study the problem of multiple hypothesis testing for multidimensional data when inter-correlations are present. The problem of multiple comparisons is common in many applications. When the data is multivariate and correlated, existing…
Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial multifractal time series of three different binomial parameters and find that the WTMM method indicates an enhanced difference between the fractal components than…
We introduce a novel online multitask setting. In this setting each task is partitioned into a sequence of segments that is unknown to the learner. Associated with each segment is a hypothesis from some hypothesis class. We give algorithms…
Large Language Model (LLM) agents are increasingly expected to maintain coherent, long-term personalized memory, yet current benchmarks primarily measure static fact retrieval, overlooking the ability to revise stored beliefs when new…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
Fractionally integrated time series, exhibiting long memory with slowly decaying autocorrelations, are frequently encountered in economics, finance, and related fields. Since the seminal work of Robinson (1995), a variety of semiparametric…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…
This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
As Multimodal Large Language Models (MLLMs) develop, their potential security issues have become increasingly prominent. Machine Unlearning (MU), as an effective strategy for forgetting specific knowledge in training data, has been widely…
It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long…
We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…
In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless It\^{o}-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high…
We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and…