Autoregressive time series models of order
p have
p
+
2
parameters, the mean, the variance of the white noise and the
p autoregressive parameters. Change in any of these over time is a sign of ...disturbance that is important to detect. The methods of this paper can test for change in any one of these
p
+
2
parameters separately, or in any collection of them. They are available in forms that make one-sided tests possible, furthermore, they can be used to test for a temporary change. The test statistics are based on the efficient score vector. The large sample properties of the change-point estimator are also explored.
The use of the efficient score statistic in sequential monitoring procedures is reviewed and analysed. Various models that arise in applications are considered. The efficient score vector has the ...same optimality property as the generalized likelihood ratio, but it has a simple-structure requiring fewer estimations, and this is especially important when the data have a complicated structure. Furthermore, with the efficient score vector it is possible to detect which component of the parameter vector is different from the hypothetical or the historical value. The problems we solve here were the subjects of separate publications, but with the new methodology they are easily calculated examples.
Sequential tests that are generalizations of Page’s CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series ...model. These tests accommodate nuisance parameters. They are based on large sample approximations to the efficient score vector under the null hypothesis of no change and under the alternative. The empirical power of the tests is evaluated in a simulation study. The new method performs better than the existing ones found in the literature if the criterion is the type I error probability, which can be unacceptably high for methods that minimize the expected value of the reaction time.
Detection of changes in health care performance, financial markets, and industrial processes have recently gained momentum due to the increased availability of complex data in real-time. As a ...consequence, there has been a growing demand in developing statistically rigorous methodologies for change-point detection in various types of data. In many practical situations, the data being monitored for the purpose of detecting changes are autocorrelated binary time series. We propose a new statistical procedure based on the partial likelihood score process for the retrospective detection of change in the coefficients of a logistic regression model with AR(p)-type autocorrelations. We carry out some Monte Carlo experiments to evaluate the power of the detection procedure as well as its probability of false alarm (type I error). We illustrate the utility using data on 30-day mortality rates after cardiac surgery and to data on IBM share transactions.
•Retrospective, or off-line change detection procedures are proposed for autocorrelated binary time series.•The test statistic is based on the standardized multidimensional partial efficient score process.•Logistic regression describes the relationship between the parameters and the binary responses.•Examples on surgeon performance and IBM transactions data demonstrate the easy applicability.•Monte Carlo experiments show excellent control over the type I error and the power properties.
A new test for detecting a change in linear regression parameters assuming a general weakly dependent error structure is given. It extends earlier methods based on cumulative sums assuming ...independent errors. The novelty is in the new standardization method and in smoothing when the time series is dominated by high frequencies. Simulations show the excellent performance of the test. Examples are taken from environmental applications. The algorithm is easy to implement. Testing for multiple changes can be done by segmentation. Nous présentons un nouveau test pour détecter le changement dans les paramètres d'une régression linéaire en supposant une structure de dépendance faible sur les erreurs. Il généralise les méthodes précédentes qui sont basées sur les sommes cumulatives et qui supposent des erreurs indépendantes. La nouveauté réside dans la nouvelle méthode de standardisation et dans le lissage lorsque la série chronologique est dominée par les hautes fréquences. Des simulations illustrent l'excellente performance de ce test. Des exemples provenant d'applications environnementales sont aussi présentés. De plus, l'algorithme est facile à implanter. Un test pour des changements multiples peut être obtenu par segmentation.
The aim of this paper is to propose methods of detecting change in the coefficients of a multinomial logistic regression model for categorical time series offline. The alternatives to the null ...hypothesis of stationarity can be either the hypothesis that it is not true, or that there is a temporary change in the sequence. We use the efficient score vector of the partial likelihood function. This has several advantages. First, the alternative value of the parameter does not have to be estimated; hence, we have a procedure that has a simple structure with only one parameter estimation using all available observations. This is in contrast with the generalized likelihood ratio-based change point tests. The efficient score vector is used in various ways. As a vector, its components correspond to the different components of the multinomial logistic regression model's parameter vector. Using its quadratic form a test can be defined, where the presence of a change in any or all parameters is tested for. If there are too many parameters one can test for any subset while treating the rest as nuisance parameters. Our motivating example is a DNA sequence of four categories, and our test result shows that in the published data the distribution of the four categories is not stationary.
Surveillance of health care performance indicators is of growing interest as drugs need to be monitored even after they passed phase 3 clinical trials and are on the market. Individuals in small ...subpopulations may still have adverse reaction to it, and even if no such adverse reaction is present, monitoring is the only way public concerns can be settled. We compare methods using large sample approximations and exact distributions for the likelihood ratio and show that the efficient score vector is just as effective tool. Furthermore, we demonstrate that it can be applied even for data structures that are too complicated for the likelihood ratio. All new monitoring schemes are simple and they can be represented by simple graphs.
We consider several procedures to detect changes in the mean or the covariance structure of a linear process. The tests are based on the weighted CUSUM process. The limit distributions of the test ...statistics are derived under the no change null hypothesis. We develop new strong and weak approximations for the sample mean as well as the sample correlations of linear processes. A small Monte Carlo simulation illustrates the applicability of our results.
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