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Cramér's moderate deviations for the LS estimator of the autoregressive processes in the neighborhood of the unit root

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STATISTICS & PROBABILITY LETTERS 2024年 209卷

作者： Miao, Yu Yin, Qing Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Henan Province Peoples R China Henan Normal Univ Henan Engn Lab Big Data Stat Anal & Optimal Contro Xinxiang 453007 Henan Province Peoples R China

In this paper, we consider the linear autoregressive model with varying coefficient theta n stending to the unit root. Cram & eacute;r's moderate deviations of the least-squares estimator of the parameter thet... 详细信息

关键词： Cram & eacute r's moderate deviations autoregressive processes Unit root

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Forecasting UK consumer price inflation with RaGNAR: Random generalised network autoregressive processes

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International Journal of Forecasting 2025年

作者： Nason, Guy P. Palasciano, Henry Antonio Department of Mathematics Imperial College London SW7 2AZ London United Kingdom

This article forecasts consumer price index (CPI) inflation in the United Kingdom using random generalised network autoregressive (RaGNAR) processes. More specifically, we fit generalised network autoregressive (GNAR) processes to a large set of random networks generated according to the Erdős–Rényi–Gilbert model and select the best-performing networks each month to compute out-of-sample forecasts. RaGNAR significantly outperforms traditional benchmark models across all horizons. Remarkably, RaGNAR also delivers materially more accurate predictions than the Bank of England's four to six month inflation rate forecasts published in their quarterly Monetary Policy Reports. Our results are remarkable not only for their accuracy, but also because of their speed, efficiency, and simplicity compared to the Bank's current forecasting processes. RaGNAR's performance improvements manifest in terms of both their root mean squared error and mean absolute percentage error, which measure different, but crucial, aspects of the methods’ performance. GNAR processes demonstrably predict future changes to CPI inflation more accurately and quickly than the benchmark models, especially at medium- to long-term forecast horizons, which is of great importance to policymakers charged with setting interest rates. We find that the most robust forecasts are those which combine the predictions from multiple GNAR processes via the use of various model averaging techniques. By analysing the structure of the best-performing graphs, we are also able to identify the key components that influence inflation rates during different periods. © 2025 The Author(s)

关键词： autoregressive processes CPI disaggregated series Forecasting Graphs Inflation Statistical learning

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On two classes of reflected autoregressive processes

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JOURNAL OF APPLIED PROBABILITY 2020年第2期57卷 657-678页

作者： Boxma, Onno Loepker, Andreas Mandjes, Michel Eindhoven Univ Technol Dept Math & Comp Sci POB 513 NL-5600 MB Eindhoven Netherlands HTW Dresden Dresden Germany Univ Amsterdam Korteweg de Vries Inst Math Sci Pk 904 NL-1098 XH Amsterdam Netherlands Univ Appl Sci Hsch Tech & Wirtschaft Friedrich List Pl 1 D-01069 Dresden Germany

We introduce two general classes of reflected autoregressive processes, INGAR(+)and GAR(+). Here, INGAR(+)can be seen as the counterpart of INAR(1) with general thinning and reflection being imposed to keep the process non-negative;GAR(+)relates to AR(1) in an analogous manner. The two processes INGAR(+)and GAR(+)are shown to be connected via a duality relation. We proceed by presenting a detailed analysis of the time-dependent and stationary behavior of the INGAR(+)process, and then exploit the duality relation to obtain the time-dependent and stationary behavior of the GAR(+)process.

关键词： INAR(1) AR(1) autoregressive processes reflection generating functions time-dependent behavior stationarity

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FINITE SAMPLE DEVIATION AND VARIANCE BOUNDS FOR FIRST ORDER autoregressive processes

FINITE SAMPLE DEVIATION AND VARIANCE BOUNDS FOR FIRST ORDER ...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Gonzalez, Rodrigo A. Rojas, Cristian R. KTH Royal Inst Technol Div Decis & Control Syst Stockholm Sweden

ISBN: (纸本)9781509066315

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by at least a positive epsilon from its true value. Our results consider both stable and unstable processes. Afterwards, we obtain problem-dependent non-asymptotic bounds on the variance of this estimator, valid for sample sizes greater than or equal to seven. Via simulations we analyze the conservatism of our bounds, and show that they reliably capture the true behavior of the quantities of interest.

关键词： autoregressive processes Non-Asymptotic Estimation Least Squares Finite Sample Analysis

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A Finite-Sample Deviation Bound for Stable autoregressive processes 2

A Finite-Sample Deviation Bound for Stable Autoregressive Pr...

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2nd Annual Conference on Learning for Dynamics and Control (L4DC)

作者： Gonzalez, Rodrigo A. Rojas, Cristian R. KTH Royal Inst Technol Div Decis & Control Syst Stockholm Sweden

In this paper, we study non-asymptotic deviation bounds of the least squares estimator for Gaussian AR(n) processes. By relying on martingale concentration inequalities and a tail-bound for similar to 2 distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR(n) process. We discuss extensions and limitations of our approach.

关键词： autoregressive processes Non-Asymptotic Estimation Least Squares Finite Sample Analysis

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Analytical Formulation of Bubble Entropy for autoregressive processes

Analytical Formulation of Bubble Entropy for Autoregressive ...

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Conference of the European Study Group on Cardiovascular Oscillations

作者： Matteo Bodini Massimo Walter Rivolta George Manis Roberto Sassi Università degli Studi di Milano Via Celoria 18 Milano Italy University of Ioannina Ioannina Greece

ISBN: (数字)9781728157511

ISBN: (纸本)9781728157528

Bubble Entropy is a recently proposed entropy metric, that is almost free of parameters. Up to date, only an operational formulation of Bubble Entropy was available. In this paper, we derived analytical formulations of Bubble Entropy for embedding dimensions m ≤ 3, when the time series is generated by a stationary Gaussian autoregressive process. Such formulations match with the estimates obtained using Monte Carlo simulations. The study allows to further investigate the mathematical properties of Bubble Entropy on stationary autoregressive processes.

关键词： Entropy Heart rate variability Time series analysis Correlation Biomedical measurement autoregressive processes

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Jeffrey's divergence between autoregressive processes disturbed by additive white noises

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SIGNAL PROCESSING 2018年 149卷 162-178页

作者： Legrand, L. Grivel, E. Thales Syst Aeroportes SA 75-77 Ave Marcel Dassault F-33700 Merignac France Univ Bordeaux IMS UMR Bordeaux INP ENSEIRB MATMECA CNRS 5218 351 Cours Liberat F-33405 Talence France

Jeffrey's divergence (JD), which is the symmetric version of the Kullback-Leibler divergence, has been used in a wide range of applications, from change detection to clutter homogeneity analysis in radar processing. It has been calculated between the joint probability density functions of successive values of autoregressive (AR) processes. In this case, the JD is a linear function of the variate number to be considered. Knowing the derivative of the JD with respect to the number of variates is hence enough to compare noise-free AR processes. However, the processes can be disturbed by additive uncorrelated white noises. In this paper, we suggest comparing two noisy 1st-order AR processes. For this purpose, the JD is expressed from the JD between noise-free AR processes and the bias the noises induce. After a transient period, the derivative of this bias with respect to the variate number becomes constant as well as the derivative of the JD. The resulting asymptotic JD increment is then used to compare noisy AR processes. Some examples illustrate this theoretical analysis. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Jeffrey's divergence autoregressive processes Kullback-Leibler divergence

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Generalizations of Nonanticipative Rate Distortion Function to Multivariate Nonstationary Gaussian autoregressive processes

Generalizations of Nonanticipative Rate Distortion Function ...

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IEEE Conference on Decision and Control

作者： Charalambos D. Charalambous Christos Kourtellaris Themistoklis Charalambous Jan H. van Schuppen Department of Electrical and Computer Engineering University of Cyprus Nicosia Cyprus Department of Electrical Engineering and Automation School of Electrical Engineering Aalto University Espoo Finland company Van Schuppen Control Research Amsterdam Netherlands

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

The characterizations of nonanticipative rate distortion function (NRDF) on a finite horizon are generalized to nonstationary multivariate Gaussian order L autoregressive, AR(L), source processes, with respect to mean square error (MSE) distortion functions. It is shown that the optimal reproduction distributions are induced by a reproduction process, which is a linear function of the state of the source, its best mean-square error estimate, and a Gaussian random process.

关键词： Rate distortion theory autoregressive processes Gaussian processes Mean square error methods Random processes

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Sparse Transition Matrix Estimation for Sub-Gaussian autoregressive processes with Missing Data

Sparse Transition Matrix Estimation for Sub-Gaussian Autoreg...

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American Control Conference

作者： Jalali, Amin Willett, Rebecca Wisconsin Inst Discovery Optimizat Theme Madison WI 53715 USA Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA Wisconsin Inst Discovery Madison WI USA

ISBN: (纸本)9781538654286

High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in statistics, control, and machine learning. In this work, we consider a high-dimensional estimation problem where a dynamical system, governed by a stable vector autoregressive model, is randomly and only partially observed at each time point. Our task amounts to estimating the transition matrix, which is assumed to be sparse. In such a scenario, where covariates are highly interdependent and partially missing, new theoretical challenges arise. While transition matrix estimation in vector autoregressive models has been studied previously, the missing data scenario requires separate efforts. Moreover, while transition matrix estimation can be studied from a high dimensional sparse linear regression perspective, the covariates are highly dependent and existing results on regularized estimation with missing data from i.i.d. covariates are not applicable. At the heart of our analysis lies 1) a novel concentration result when the innovation noise satisfies the convex concentration property, as well as 2) a new quantity for characterizing the interactions of the time-varying observation process with the underlying dynamical system.

关键词： Sparse matrices Technological innovation Estimation autoregressive processes Optimization Data models Covariance matrices"

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PREDICTION-BASED SIMILARITY IDENTIFICATION FOR autoregressive processes

PREDICTION-BASED SIMILARITY IDENTIFICATION FOR AUTOREGRESSIV...

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IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Wu, Hanwei Wang, Qiwen Flierl, Markus KTH Royal Inst Technol Sch Elect Engn & Comp Sci Stockholm Sweden

ISBN: (纸本)9781728112954

The task of similarity identification is to identify items in a database which are similar to a given query item for a given metric. The identification rate of a compression scheme characterizes the minimum rate that can be achieved which guarantees reliable answers with respect to a given similarity threshold [1]. In this paper, we study a prediction-based quadratic similarity identification for autoregressive processes. We use an ideal linear predictor to remove linear dependencies in autoregressive processes. The similarity identification is conducted on the residuals. We show that the relation between the distortion of query and database processes and the distortion of their residuals is characterized by a sequence of eigenvalues. We derive the identification rate of our prediction-based approach for autoregressive Gaussian processes. We characterize the identification rate for the special case where only the smallest value in the sequence of eigenvalues is required to be known and derive its analytical upper bound by approximating a sequence of matrices with a sequence of Toeplitz matrices.

关键词： Databases Eigenvalues and eigenfunctions autoregressive processes Symmetric matrices Distortion Upper bound Gaussian processes

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