Robust estimation procedure for autoregressive models with heterogeneity

Journal article


Callens, A., Wang, Y.-G., Fu, L. and Liquet, B.. (2021). Robust estimation procedure for autoregressive models with heterogeneity. Environmental Modeling and Assessment. 26(3), pp. 313-323. https://doi.org/10.1007/s10666-020-09730-w
AuthorsCallens, A., Wang, Y.-G., Fu, L. and Liquet, B.
Abstract

In environmental studies, regression analysis is frequently performed. The classical approach is the ordinary least squares method which consists in minimizing the sum of the squares of the residuals. However, this method relies on strong assumptions that are not always satisfied. In environmental data, the response variable often contains outliers and errors can be heteroscedastic. This can have significant effects on parameter estimation. To solve this problem, the weighted M-estimation was developed. It assumes a parametric function for the variance, and, estimates alternately and robustly, mean and variance parameters. However, this method is limited to the independent errors case, and is not applicable to time series data. Therefore, we introduce a new estimation procedure which adapts the weighted M-estimation to environmental time series data, while selecting optimal value for the tuning parameter present in the M-estimation. We compare the efficiency of our procedure on simulated data to other usual regression methods. Our estimation procedure outperforms the other methods providing estimates with lower biases and mean squared errors. Finally, we illustrate the proposed method using an air quality dataset from Beijing. This method has been implemented in the R package RlmDataDriven.

Keywordsheteroscedasticy; model selection; robust estimation; temporal correlations
Year2021
JournalEnvironmental Modeling and Assessment
Journal citation26 (3), pp. 313-323
PublisherSpringer
ISSN1420-2026
Digital Object Identifier (DOI)https://doi.org/10.1007/s10666-020-09730-w
Scopus EID2-s2.0-85091780535
Page range313-323
FunderAustralian Research Council (ARC)
National Natural Science Foundation of China (NSFC)
Fundamental Research Funds for the Central Universities
Shaanxi Province, China
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online01 Oct 2020
Publication process dates
Accepted24 Aug 2020
Deposited11 Dec 2022
ARC Funded ResearchThis output has been funded, wholly or partially, under the Australian Research Council Act 2001
Grant IDDP160104292
11871390
xjj2017180
2018JQ1006
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