English
Related papers

Related papers: Functional Periodic ARMA Processes

200 papers

We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map…

Statistics Theory · Mathematics 2013-02-14 Arash A. Amini , Martin J. Wainwright

In this article, we use the generating functions of the Humbert polynomials to define two types of Humbert generalized fractional differenced ARMA processes. We present stationarity and invertibility conditions for the introduced models.…

Statistics Theory · Mathematics 2023-08-09 Niharika Bhootna , Monika Singh Dhull , Arun Kumar , Nikolai Leonenko

In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The…

Computation · Statistics 2016-09-09 Javier E. Contreras-Reyes , Wilfredo Palma

AutoRegressive Conditional Heteroscedasticity (ARCH) models are standard for modeling time series exhibiting volatility, with a rich literature in univariate and multivariate settings. In recent years, these models have been extended to…

Methodology · Statistics 2026-03-19 Alexander Aue , Sebastian Kühnert , Gregory Rice , Jeremy VanderDoes

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…

Methodology · Statistics 2023-12-12 J. Klepsch , C. Klüppelberg , T. Wei

Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for…

Methodology · Statistics 2025-10-28 Jesse Wheeler , Edward L. Ionides

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…

Applications · Statistics 2010-11-29 Valderio A. Reisen , Wilfredo Palma , Josu Arteche , Bartolomeu Zamprogno

We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…

Methodology · Statistics 2020-12-01 Daren Wang , Zifeng Zhao , Rebecca Willett , Chun Yip Yau

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…

Statistics Theory · Mathematics 2015-12-18 Anders Lindquist , Giorgio Picci

The classical functional linear regression model (FLM) and its extensions, which are based on the assumption that all individuals are mutually independent, have been well studied and are used by many researchers. This independence…

Computation · Statistics 2018-11-02 Tingting Huang , Gilbert Saporta , Huiwen Wang , Shanshan Wang

An emerging number of modern applications involve forecasting time series data that exhibit both short-time dynamics and long-time seasonality. Specifically, time series with multiple seasonality is a difficult task with comparatively fewer…

Machine Learning · Computer Science 2020-08-31 Tianyang Xie , Jie Ding

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…

Methodology · Statistics 2018-06-22 Fábio M. Bayer , Renato J. Cintra , Francisco Cribari-Neto

In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA…

Methodology · Statistics 2022-04-11 Israel Martínez-Hernández , Marc G. Genton

In this paper we investigate the dependence structure for PARMA models (i.e. ARMA models with periodic coefficients) with symmetric alpha-stable innovations. In this case the covariance function is not defined and therefore other measures…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Joanna Nowicka-Zagrajek , Agnieszka Wylomanska

In this paper, we introduce the concept of fractional integration for spatial autoregressive models. We show that the range of the dependence can be spatially extended or diminished by introducing a further fractional integration parameter…

Methodology · Statistics 2023-09-14 Philipp Otto , Philipp Sibbertsen

We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…

Probability · Mathematics 2019-12-23 Akihiko Inoue

Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent years. However, these models are used mainly as a statistical…

Data Analysis, Statistics and Probability · Physics 2017-03-20 Jakub Ślęzak , Aleksander Weron

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…

Methodology · Statistics 2021-05-13 Tingguo Zheng , Han Xiao , Rong Chen

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where…

Statistics Theory · Mathematics 2013-01-22 Peter J. Brockwell , Vincenzo Ferrazzano , Claudia Klüppelberg

The Unit-Lindley is a one-parameter family of distributions in $(0,1)$ obtained from an appropriate transformation of the Lindley distribution. In this work, we introduce a class of dynamical time series models for continuous random…

Statistics Theory · Mathematics 2025-04-11 Guilherme Pumi , Danilo Hiroshi Matsuoka , Taiane Schaedler Prass