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Time series forecasting (TSF) is essential in various domains, and recent advancements in diffusion-based TSF models have shown considerable promise. However, these models typically adopt traditional diffusion patterns, treating TSF as a…

Machine Learning · Computer Science 2024-12-13 Jiaxin Gao , Qinglong Cao , Yuntian Chen

This paper proposes a simple yet effective convolutional module for long-term time series forecasting. The proposed block, inspired by the Auto-Regressive Integrated Moving Average (ARIMA) model, consists of two convolutional components:…

Machine Learning · Computer Science 2025-09-15 Myung Jin Kim , YeongHyeon Park , Il Dong Yun

The {\alpha}-stable L\'evy process, commonly used to describe L\'evy flight, is characterized by discontinuous jumps and is widely used to model anomalous transport phenomena. In this study, we investigate the associated exit problem and…

Numerical Analysis · Mathematics 2026-01-16 Minglei Yang , Diego del-Castillo-Negrete , Guannan Zhang

In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily…

Statistics Theory · Mathematics 2022-06-22 Samir Ben Hariz , Alexandre Brouste , Youssef Esstafa , Marius Soltane

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

Probability · Mathematics 2024-11-21 Paweł J. Szabłowski

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time series temperature uncertainty model which is the Auto-regressive Moving Average (ARMA)(1, 1)…

Methodology · Statistics 2023-03-06 Mahmud Hasan , Gauree Wathodkar , Mathias Muia

We give a new definition of a L\'{e}vy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of…

Probability · Mathematics 2019-04-08 David Berger

Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…

Probability · Mathematics 2022-04-20 G. L. Feltes , S. R. C. Lopes

The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations…

Methodology · Statistics 2023-02-15 Shu Wei Chou-Chen , Pedro A. Morettin

In this article, we introduce a Gegenbauer autoregressive tempered fractionally integrated moving average (GARTFIMA) process. We work on the spectral density and autocovariance function for the introduced process. The parameter estimation…

Statistics Theory · Mathematics 2022-08-31 Niharika Bhootna , Arun Kumar

We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…

Probability · Mathematics 2021-04-29 Annemarie Bitter , Robert Stelzer , Bennet Ströh

The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way…

Methodology · Statistics 2023-04-14 Yangyang Chen , Pedro Alberto Morettin , Chang Chiann

The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…

Probability · Mathematics 2018-08-20 Mikkel Slot Nielsen , Jan Pedersen

This paper presents an algorithm for the simulation of Hawkes-type processes where the intensity is expressed in terms of a continuous-time autoregressive moving average model. We identify upper bounds for both the univariate and the…

Computation · Statistics 2025-06-10 Lorenzo Mercuri , Andrea Perchiazzo , Edit Rroji

For each $\lambda>0$ and every square-integrable infinitely-divisible (ID) distribution there exists at least one stationary stochastic process $t\mapsto X_t$ with the specified distribution for $X_1$ and with first-order autoregressive…

Probability · Mathematics 2021-06-02 Robert L Wolpert

This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval $(0,1)$. The model extends the unit-log-symmetric family by introducing a quantile-based…

Computation · Statistics 2026-05-26 Helton Saulo , Roberto Vila , Filidor Vilca

In this work we introduce the class of unit-Weibull Autoregressive Moving Average models for continuous random variables taking values in $(0,1)$. The proposed model is an observation driven one, for which, conditionally on a set of…

Statistics Theory · Mathematics 2025-04-29 Guilherme Pumi , Taiane Schaedler Prass , Cleiton Guollo Taufemback

In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…

Statistics Theory · Mathematics 2021-07-30 Niharika Bhootna , Arun Kumar

In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…

We propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations…

Econometrics · Economics 2022-02-25 José E. Figueroa-López , Ruoting Gong , Yuchen Han