Moderate deviations for the mildly stationary autoregressive model with dependent errors

IF 1.2 4区数学 Q2 STATISTICS & PROBABILITY

Statistics Pub Date : 2023-11-06 DOI:10.1080/02331888.2023.2278034

Hui Jiang, Guangyu Yang, Mingming Yu

引用次数: 0

Abstract

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale methods, we establish the moderate deviations for the least squares estimators of the regressor and error, which can be applied to understand the near-integrated second order autoregressive processes. As an application, we also obtain the moderate deviations for the Durbin-Watson statistic.

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具有相关误差的轻度平稳自回归模型的中等偏差

本文研究了一类具有相关误差的温和平稳一阶自回归(AR(1))模型参数的归一化最小二乘估计，该模型被建模为温和平稳AR(1)过程。利用鞅方法，建立了回归量和误差的最小二乘估计的中等偏差，可用于理解近积分二阶自回归过程。作为应用，我们也得到了Durbin-Watson统计量的中等偏差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics 数学-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.