A note on influence diagnostics in AR(1) time series models

被引:13
作者
Zevallos, Mauricio [1 ]
Santos, Bruno
Hotta, Luiz K. [1 ]
机构
[1] Univ Estadual Campinas, Dept Stat, IMECC UNICAMP, BR-13083859 Campinas, SP, Brazil
基金
巴西圣保罗研究基金会;
关键词
Slope; Curvature; Local influence; Outliers; LOCAL INFLUENCE; REGRESSION-MODELS; GARCH PROCESSES;
D O I
10.1016/j.jspi.2012.05.004
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The purpose of this paper is to develop influence diagnostics for AR(1) models under the innovative and the data perturbation schemes. There are four main contributions. First, we derive analytical expressions for the slope and curvature statistics. Second, we establish a relationship between the slope and curvature showing that the standardised slope and standardised curvature are equal for the innovative perturbation scheme, and these vectors are nearly identical for several values of the autoregressive parameter, for the data perturbation scheme. Third, we present a connection between the influence statistics and the tests for outlier detection. Fourth, for the innovative perturbation scheme, we derive the asymptotic distribution of a new influence statistic, whereas for the data perturbation scheme, the distribution of the influence statistics is obtained via Monte Carlo simulation. We additionally discuss practical guidelines for the use of local influence statistics, which are illustrated on a chemical process data set. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码:2999 / 3007
页数:9
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