Time Series Analysis: Research on Data Modeling Methods

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 3973

Special Issue Editors


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Guest Editor
School of Mathematics and Statistics, Liaoning University, Shenyang, China
Interests: mathematical statistics; time series analysis; risk theory

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Guest Editor
School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Interests: mathematical statistics; time series analysis; high-dimensional data analysis; Bayesian analysis

Special Issue Information

Dear Colleagues,

The earliest time series analysis can be traced back to ancient Egypt 7000 years ago. The ancient Egyptians recorded the rise and fall of the Nile from day to day to form a time series. Since the autoregressive model was proposed by British statistician G. U. Yule in the early part of the last century, time series analysis has become a popular research direction for its wide application in the fields of economy, finance, engineering, and many others.

The aim of this Special Issue is to bring together papers on the following topics:

  • Innovation in time series models (any type of time series models, such as covariate-driven time series models, measurement error models, etc.).
  • Research on inference problems of time series models (including but not limited to model selection, parameter estimation, testing problems, etc.).
  • The application of time series models and methods in prediction, change point detection and other practical problems.
  • This Special Issue also aims to include interdisciplinary research or excellent comprehensive review papers, preferably with time series models or methods as the core contribution. In particular, articles containing practical applications will be very welcome.

In addition, mathematical research that can be applied to solving statistical problems is welcome.

Dr. Dehui Wang
Dr. Kai Yang
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • time series model
  • statistic inference method
  • measurement error
  • interdisciplinary application
  • statistical research

Published Papers (4 papers)

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Research

17 pages, 4159 KiB  
Article
Estimation of Random Coefficient Autoregressive Model with Error in Covariates
by Xiaolei Zhang, Jin Chen and Qi Li
Axioms 2024, 13(5), 303; https://doi.org/10.3390/axioms13050303 - 2 May 2024
Viewed by 534
Abstract
Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covariates. The least squares and weighted least squares methods are [...] Read more.
Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covariates. The least squares and weighted least squares methods are used to estimate the model parameters, and the consistency and asymptotic normality of the two kinds of estimators are proved. Furthermore, we propose an empirical likelihood method based on weighted score equations to construct confidence regions for the parameters. The simulation results show that the weighted least squares estimators are superior to the least squares estimators and that the confidence regions have good finite-sample behavior. At last, the model is applied to a real data example. Full article
(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
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21 pages, 454 KiB  
Article
Randomness Test of Thinning Parameters for the NBRCINAR(1) Process
by Shuanghong Zhang
Axioms 2024, 13(4), 260; https://doi.org/10.3390/axioms13040260 - 14 Apr 2024
Viewed by 696
Abstract
Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed [...] Read more.
Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed by the negative binomial thinning operator with random coefficients, to address the problem of constant thinning parameters which might not always accurately represent real-world settings because of numerous external and internal causes. We estimate the model parameters of interest by the two-step conditional least squares method, obtain the asymptotic behaviors of the estimators, and furthermore devise a technique to test the constancy of the thinning parameters, which is essential for determining whether or not the proposed model should consider the parameters’ randomness. The effectiveness and dependability of the suggested approach are illustrated by a series of thorough simulation studies. Finally, two real-world data analysis examples reveal that the suggested approach is very useful and flexible for applications. Full article
(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
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20 pages, 1433 KiB  
Article
Portmanteau Test for ARCH-Type Models by Using High-Frequency Data
by Yanshan Chen, Xingfa Zhang, Chunliang Deng and Yujiao Liu
Axioms 2024, 13(3), 141; https://doi.org/10.3390/axioms13030141 - 22 Feb 2024
Viewed by 919
Abstract
The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this [...] Read more.
The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this paper. Simulation results show that the empirical size and power of the modified test statistics of the model using high-frequency data are better than those of the daily model. Three stock indices (CSI 300, SSE 50, CSI 500) are taken as an example to illustrate the practical application of the test. Full article
(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
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17 pages, 396 KiB  
Article
A Two-Step Estimation Method for a Time-Varying INAR Model
by Yuxin Pang, Dehui Wang and Mark Goh
Axioms 2024, 13(1), 19; https://doi.org/10.3390/axioms13010019 - 27 Dec 2023
Viewed by 994
Abstract
This paper proposes a new time-varying integer-valued autoregressive (TV-INAR) model with a state vector following a logistic regression structure. Since the autoregressive coefficient in the model is time-dependent, the Kalman-smoothed method is applicable. Some statistical properties of the model are established. To estimate [...] Read more.
This paper proposes a new time-varying integer-valued autoregressive (TV-INAR) model with a state vector following a logistic regression structure. Since the autoregressive coefficient in the model is time-dependent, the Kalman-smoothed method is applicable. Some statistical properties of the model are established. To estimate the parameters of the model, a two-step estimation method is proposed. In the first step, the Kalman-smoothed estimation method, which is suitable for handling time-dependent systems and nonstationary stochastic processes, is utilized to estimate the time-varying parameters. In the second step, conditional least squares is used to estimate the parameter in the error term. This proposed method allows estimating the parameters in the nonlinear model and deriving the analytical solutions. The performance of the estimation method is evaluated through simulation studies. The model is then validated using actual time series data. Full article
(This article belongs to the Special Issue Time Series Analysis: Research on Data Modeling Methods)
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