Adaptive estimation of autoregression models under long-tailed symmetric distribution

Date

2022-01-01

Author

Yentür, Begüm
Akkaya, Ayşen
Bayrak, Özlem Türker

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

118
views

0
downloads

© 2022 Taylor & Francis Group, LLC.Non-normal innovations in autoregression models frequently occur in practice. In this situation, least squares (LS) estimators are known to be inefficient and non-robust, and maximum likelihood (ML) estimators need to be solved numerically, which becomes a daunting task. In the literature, the modified maximum likelihood (MML) estimation technique has been proposed to obtain the estimators of model parameters. While an explicit solution can be found via this method, the requirement of knowing the shape parameter becomes a drawback, especially in machine learning. In this study, we use the adaptive modified maximum likelihood (AMML) methodology, which combines the MML with Huber’s M-estimation so that this assumption is relaxed. The performance of the method in terms of efficiency and robustness is analyzed via simulation and compared to LS, MML and ML estimates that are obtained numerically via the Expectation Conditional Maximization (ECM) algorithm. Test statistics are proposed for the crucial parameters of the model. The results show that the AMML estimators are preferable in most of the settings according to the mean squared error (MSE) criterion and the test statistics based on AMML method are more robust than the others. Furthermore, both real life and synthetic data examples are given.

Subject Keywords

Autoregressive models, Adaptive modified Maximum likelihood, Efficiency, Robustness, Hypothesis testing, LINEAR-REGRESSION MODEL, MAXIMUM-LIKELIHOOD, ROBUST ESTIMATION, PARAMETERS, LOCATION, Adaptive modified Maximum likelihood, Autoregressive models, Efficiency, Hypothesis testing, Robustness

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85135268639&origin=inward
https://hdl.handle.net/11511/99128

Journal

Communications in Statistics: Simulation and Computation

DOI

https://doi.org/10.1080/03610918.2022.2103568

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Robust estimation in multiple linear regression model with non-Gaussian noise Akkaya, Ayşen (2008-02-01) The traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies. To rectify the situation we propose a reparametrization of the model. We derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies.
Adaptive inference of autoregressive models under nonnormality Yentür, Begüm; Dener Akkaya, Ayşen.; Department of Statistics (2019) Recently, non-normal innovations in autoregressive models have become prevalent in many applications. In this case, it is known that the least squares (LS) estimators are neither efficient nor robust. Also, obtaining maximum likelihood (ML) estimators requires numerical solution which is a formidable task. To overcome these difficulties modified maximum likelihood (MML) estimation technique is used to obtain the estimators of the model parameters. In this method, although explicit solution can be found, the...
Nonlinear modeling and vibration analysis of horizontal drum type washing machines Baykal, Cem; Yazıcıoğlu, Yiğit; Department of Mechanical Engineering (2019) Nonlinear two and three-dimensional dynamical models for horizontal drum type washing machines are developed considering rotating unbalance type excitation. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using the Harmonic Balance Method (HBM). The resulting nonlinear algebraic equations are solved by using Newton’s method with arc-length continuation. Several case studies are performed in order to observe the effects of orientation angles of springs ...
Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations Akkaya, Ayşen (2001-01-01) The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] who give solutions for a simple AR(I) model
Hybrid wavelet-neural network models for time series data Kılıç, Deniz Kenan; Uğur, Ömür; Department of Financial Mathematics (2021-3-3) The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (∧GSPC) and NASDAQ (∧ IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. ...

Citation Formats

B. Yentür, A. Akkaya, and Ö. T. Bayrak, “Adaptive estimation of autoregression models under long-tailed symmetric distribution,” Communications in Statistics: Simulation and Computation, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85135268639&origin=inward.