Hybrid regions for post-change mean in a sequence of normal variables

The hybrid bootstrap uses resampling ideas to extend the duality approach to the interval estimation for a parameter of interest when there are nuisance parameters. The confidence region constructed by the hybrid bootstrap may perform much better than the ordinary bootstrap region in a situation where the data provide substantial information about the nuisance parameter, but limited information about the parameter of interest. We apply this method to estimate the post-change mean after a change is detected by a stopping procedure in a sequence of independent normal variables. Since distribution theory in change point problems is generally a challenge, we use bootstrap simulation to find empirical distributions of test statistics and calculate critical thresholds. Both likelihood ratio and Bayesian test statistics are considered to set confidence regions for post-change means in the normal model. In the simulation studies, the performance of hybrid regions are compared with that of ordinary bootstrap regions in terms of the widths and coverage probabilities of confidence intervals.     

A window-limited generalized likelihood ratio test for monitoring Poisson processes with linear drifts

There is gradually increasing attention devoted to the monitoring of Poisson process due to its wide applications in industry quality control and health-care surveillance. However, most of the study focuses on the case with step shifts in Poisson means. Relatively little attention has been paid to the case with linear drifts in Poisson means. This paper extends the window-limited generalized likelihood ratio (WGLR) test from the monitoring of normal means to Poisson processes, with focus on linear drifts. The comparison results with the adaptive cumulative sum (ACUSUM) charts and the weighted CUSUM (WCUSUM) charts show that the WGLR chart generally provides better detection performance than the other alternative methods in both the zero-state and steady-state cases.     

A discussion on ‘Detection of intrusions in information systems by sequential change-point methods’ by Tartakovsky, Rozovskii, Blažek, and Kim

Tartakovsky et al. provide us with, and should be thanked for, an illuminating introduction to the problems of detecting intrusions and other denial of services attacks, and a thorough discussion and analysis of the relevance of CUSUM-based change detection algorithms for this purpose.This discussion mainly addresses three issues: introducing a minimum change magnitude, adaptation and tuning of CUSUM algorithms, and processing binary quantized data. The influence of the adaptation in the NP-CUSUM algorithm on its performances is questioned.     

CUSUM method in predicting regime shifts and its performance in different stock markets allowing for transaction fees

Statistical Process Control (SPC) is a scientific approach to quality improvement in which data are collected and used as evidence of the performance of a process, organisation or set of equipment. One of the SPC techniques, the cumulative sum (CUSUM) method, first developed by E.S. Page (1961), uses a series of cumulative sums of sample data for online process control. This paper reviews CUSUM techniques applied to financial markets in several different ways. The performance of the CUSUM method in predicting regime shifts in stock market indices is then studied in detail. Research in this field so far does not take the transaction fees of buying and selling into consideration. As the study in this paper shows, the performances of the CUSUM when taking account of transaction fees are quite different to those not taking transaction fees into account. The CUSUM plan is defined by parameters h and k. Choosing the parameters of the method should be based on studies that take transaction fees into account. The performances of the CUSUM in different stock markets are also compared in this paper. The results show that the same CUSUM plan has remarkably different performances in different stock markets.     

Confidence bands for Brownian motion and applications to Monte Carlo simulation

Minimal area regions are constructed for Brownian paths and perturbed Brownian paths. While the theoretical optimal region cannot be obtained in closed form, we provide practical confidence regions based on numerical approximations and local time arguments. These regions are used to provide informal convergence assessments for both Monte Carlo and Markov Chain Monte Carlo experiments, via the Brownian asymptotic approximation of cumulative sums.     

Multiple hypothesis test for parameter constancy based on recursive residuals

This article presents a multiple hypothesis test procedure that combines two well known tests for structural change in the linear regression model, the CUSUM test and the recursive t test. The CUSUM test is run through the sequence of recursive residuals as usual; if the CUSUM plot does not violate the critical lines, one more step is taken to perform the t test for hypothesis of zero mean based on all recursive residuals. The asymptotic size of this multiple hypothesis test is derived; power simulation results suggest that it outperforms the traditional CUSUM test and complements other tests that are currently stressed in econometrics.     

CUSUM control schemes for Gaussian processes

A CUSUM control scheme for detecting a change point in a Gaussian process is derived. An upper and a lower bound for the distribution of the run length and for its moments is given. In a Monte Carlo study the average run length (ARL) of this chart is compared with the ARL of two other CUSUM procedures which are based on approximations to the sequential probability ratio, and, moreover, with EWMA schemes for autocorrelated data. Results on the optimal choice of the reference value are presented. Furthermore it is investigated how these charts behave if the model parameters are estimated.     

An empirical likelihood-based CUSUM for on-line model change detection

Abstract

In change detection problem, the distribution of a series of observations can change at some unknown instant. The aim of on-line change detection rule is to detect this change, as rapidly as possible, while ensuring a low rate of false alarm. The most popular rule to treat this problem is the Page’s CUSUM rule. The use of this rule supposes that the two distributions, before and after the change, are known, which is often restrictive in practice. In this article, a nonparametric rule is proposed. Only two learning samples, characterizing the in-control and the out-of-control functioning modes of the system, are needed to implement the rule. The new detection approach is based on the use of a well-known nonparametric method, Empirical Likelihood. Some numerical studies show the relevance of our approach, especially when the size of the learning samples are quite small.     

浙江农村居民消费支出系统函数的稳定性检验

从1983年到2007年,浙江农村居民的消费结构发生了很大的变化,但是模型参数稳定性检验表明,构成需求系统的八个消费支出等式中,只有衣着、家庭设备用品及服务、交通和通讯、文教娱乐用品及服务、杂项类消费支出五个等式发生了短暂和小幅的结构性变化,食品、居住、医疗保健类消费支出等式保持稳定。因此,总体来看,这段时期浙江农村居民的消费行为本身并没有发生显著的变化。显然,农村居民消费结构的变化主要归因于价格和收入的变化,而非偏好的变化。     

Parameter Change Test for Poisson Autoregressive Models

In this paper, we consider the problem of testing for a parameter change in Poisson autoregressive models. We suggest two types of cumulative sum (CUSUM) tests, namely, those based on estimates and residuals. We first demonstrate that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal and then construct the CMLE‐based CUSUM test. It is shown that under regularity conditions, its limiting null distribution is a function of independent Brownian bridges. Next, we construct the residual‐based CUSUM test and derive its limiting null distribution. Simulation results are provided for illustration. A real‐data analysis is performed on data for polio incidence and campylobacteriosis infections.