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Monitoring persistence change in infinite variance observations
Zhanshou Chen,Zheng Tian,Chunhui Zhao 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.1
In this paper, we adopt a kernel-weighted variance ratio statistic to monitor persistence change in infinite variance observations. We focus on a I(0) to I(1) regime switch for sequences in the domain of attraction of a stable law and local-to-finite variance sequences. The null distribution of the monitoring statistic and its consistency under alternative hypothesis are proved. In particular, a bootstrap approximation is proposed to determine the critical values for the derived asymptotic distribution depends on the unknown tail index. The small sample performance of the proposed monitoring procedures are illustrated by both simulation and application to Sweden/US foreign exchange rate data.
Monitoring parameter changes in RCA(p) models
Fuxiao Li,Zheng Tian,Peiyan Qi,Zhanshou Chen 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.1
A fluctuation monitoring procedure is proposed to detect parameter changes in randomcoefficient autoregressive models of order p (RCA(p)). It extends parameter changemonitoring to RCA(p) models. The asymptotic properties of our test statistic are derivedunder both the null of no change in parameters and the alternative of changes inparameters. The finite sample properties are investigated by a simulation study. Finally,we apply the statistic to a group of financial data. Simulation and empirical applicationdemonstrate the effectiveness of the proposed statistic.
Monitoring persistent change in a heavy-tailed sequence with polynomial trends
Peiyan Qi,Zi Jin,Zheng Tian,Zhanshou Chen 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.4
This paper considers, for the first time, sequential monitoring against a change from I(1) toI(0) in a heavy-tailed sequence with polynomial trends. To detect the persistent changequickly and powerfully, a moving kernel-weighted variance ratio statistic is proposed,which is based on the sequentially updated residual process. The null distribution ofthe monitoring statistic and its consistency under the alternative hypothesis are proved. Simulations indicate that our procedure can achieve a good performance on a finite samplefor both early change and late change. The effectiveness of the proposed procedures is welldemonstrated by two sets of financial series.