相关论文: Certain Semi-L\'evy Driven CARMA Processes: Estima…

In this paper, we use the stochastic approximation method to estimate Sliced Average Variance Estimation (SAVE). This method is known for its efficiency in recursive estimation. Stochastic approximation is particularly effective for…

Full electronic automation in stock exchanges has recently become popular, generating high-frequency intraday data and motivating the development of near real-time price forecasting methods. Machine learning algorithms are widely applied to…

In this paper we introduce the class of beta seasonal autoregressive moving average ($\beta$SARMA) models for modeling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta…

This article studies nonparametric methods to estimate the co-integrated volatility for multi-dimensional L\'evy processes with high frequency data. We construct a spectral estimator for the co-integrated volatility and prove minimax rates…

Present energy demand and modernization are leading to greater fossil fuel consumption, which has increased environmental pollution and led to climate change. Hence to decrease dependency on conventional energy sources, renewable energy…

The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the…

We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a L\'{e}vy process. The main interest of this work is to…

Two-dimensional (2-D) autoregressive moving average (ARMA) models are commonly applied to describe real-world image data, usually assuming Gaussian or symmetric noise. However, real-world data often present non-Gaussian signals, with…

Data-driven control methods need to be sample-efficient and lightweight, especially when data acquisition and computational resources are limited -- such as during learning on hardware. Most modern data-driven methods require large datasets…

We describe a simple and succinct methodology to develop hourly auto-regressive moving average (ARMA) models to forecast power output from a photovoltaic solar generator. We illustrate how to build an ARMA model, to use statistical tests to…

The stock market prediction has always been crucial for stakeholders, traders and investors. We developed an ensemble Long Short Term Memory (LSTM) model that includes two-time frequencies (annual and daily parameters) in order to predict…

One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…

Large language models (LLMs) struggle with compositional generalisation, limiting their ability to systematically combine learned components to interpret novel inputs. While architectural modifications, fine-tuning, and data augmentation…

Subspace methods like canonical variate analysis (CVA) are regression based methods for the estimation of linear dynamic state space models. They have been shown to deliver accurate (consistent and asymptotically equivalent to quasi maximum…

We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…

Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…

Assume a L\'evy process $X$ on the time interval $[0,1]$ that is an $L_2$-martingale and let $Y$ be either its stochastic exponential or $X$ itself. We consider Riemann-approximations of certain stochastic integrals driven by $Y$ and relate…

Our goal is to estimate the characteristic exponent of the input to a L\'evy-driven storage system from a sample of equispaced workload observations. The estimator relies on an approximate moment equation associated with the…

In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…