Related papers: Memory properties of transformations of linear pro…
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
In this work we present a Gaussian process that arise from the iteration of p fractional Ornstein-Uhlenbeck processes generated by the same fractional Brownian motion. This iteration results, when the values of lambdas are pairwise…
This paper explores seasonal and long-memory time series properties by using the seasonal fractional ARIMA model when the seasonal data has one and two seasonal periods and short-memory counterparts. The stationarity and invertibility…
In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…
This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function $\lambda$, given non-identically distributed realisations,…
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their…
A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that…
We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…
This paper analyzes the limit properties of the empirical process of $\alpha$-stable random variables with long range dependence. The $\alpha$-stable random variables are constructed by non-linear transformations of bivariate sequences of…
In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In…
We consider the effects of memory on the stationary behavior of a two-dimensional Langevin dynamics in a confining potential. The system is treated in an overdamped approximation and the degrees of freedom are under the influence of…
This article develops nonparametric cointegrating regression models with endogeneity and semi-long memory. We assume that semi-long memory is produced in the regressor process by tempering of random shock coefficients. The fundamental…
Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…
We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
The signature kernel is a kernel between time series of arbitrary length and comes with strong theoretical guarantees from stochastic analysis. It has found applications in machine learning such as covariance functions for Gaussian…
Martensitic transformations, viewed as continuous transformations between triply periodic minimal surfaces (TPMS), as originally proposed by Hyde and Andersson [Z. Kristallogr. 174, 225 (1986)], is extended to include paths between the…
We identify a new class of non-Hermitian causal processes that produce statistically significant temporal correlations invisible to conventional spectral methods. Using a generative model with a strictly causal memory kernel, we demonstrate…