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Rank tests for changepoint problems

变点问题的秩检验

We consider procedures based on quadratic form rank statistics to test for one or more changepoints in a series of independent observations. Models incorporating both smooth and abrupt changes are introduced. Various test statistics are suggested, their asymptotic null distributions are derived and tables of significance points are given. A Monte Carlo study shows that the asymptotic significance points are applicable to moderately sized samples.

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Tests for a change-point

变点检验

The problem considered is that of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests, such as those based on the likelihood ratio and recursive residuals, are studied. Power approximations are developed by integrating approximations for conditional boundary crossing probabilities. A comparison of several tests is made.

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Conditional bootstrap methods in the mean-shift model

均值突变模型中的条件自助法

Bootstrap methods are not inherently conditional, but they can be made so by appropriate stratification of the simulated samples which bootstrap produces. We show how stratification can work in a bootstrap analysis of mean-shift in Nile river flow data. The results are compared with both parametric and semiparametric likelihood analyses. The paper ends with some general remarks on conditional bootstraps.

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Asymptotic Inference for a Change-Point Poisson Process

变点泊松过程的渐近推断

Easily implemented asymptotic off-line procedures for the change-point Poisson process with $\lambda(t)$, the intensity at time $t$, equal to $\lambda_1$ if $t \leq \tau$ and to $\lambda_2$ if $t > \tau$, are developed. They may also be applied to a problem of estimation of the location of a discontinuity in density discussed by Chernoff and Rubin (1956). A test for change is noted, a test of the hypothesis that $\tau = \tau_0$ is proposed, and point and interval estimates…

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Optimal Stopping Times for Detecting Changes in Distributions

检测分布变化的最优停止时间

It is shown that Page's stopping time is optimal for the detection of changes in distributions, in a well defined sense. This work is a generalization of an existing result where it was shown that Page's stopping time is optimal asymptotically.

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Bayesian Model Monitoring

贝叶斯模型监测

SUMMARY A simple method of monitoring the predictive performance of a class of Bayesian models is introduced. The models involve sequential analyses of sequences of observations and are appropriate for a variety of monitoring and forecasting applications. For any given model, the monitoring technique is based on a comparison of the predictive ability of the model, measured by the observed values of predictive densities, with that of a single alternative. The alternative is…

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Monitoring and Adaptation in Bayesian Forecasting Models

贝叶斯预测模型的监控与适应

Practical aspects of a new technique for monitoring and controlling the predictive performance of Bayesian forecasting models are discussed. The basic features of the approach to model monitoring introduced in a general setting in West (1986) are described and extended to a wide class of dynamic, nonnormal, and nonlinear Bayesian forecasting models. An associated method of automatically detecting and rejecting outliers and adapting models to abrupt structural changes in the…

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The frequency of price adjustment

价格调整的频率

Data on the newsstand prices of American magazines is used to investigate the determinants of the frequency of nominal price change. Magazine price changes, often coming after real prices have fallen by one quarter, provide strong evidence for monopolistic sticky price models. The data is examined by applying a fixed effects logit specification to the price change rule implied by a target-threshold model of a firm facing general price inflation, an uncertain future and…

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Likelihood Ratio Tests for a Change in the Multivariate Normal Mean

多元正态均值变化的似然比检验

A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling T 2 for the sequences before and after the change point. The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality.…

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A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series

时间序列自激门限自回归型非线性的综合检验

A portmanteau test to detect self-exciting threshold autoregressive-type nonlinearity in time series data is proposed. The test is based on cumulative sums of standardized residuals from autoregressive fits to the data. Significance levels for the test under the hypothesis of linearity are obtain from the asymptotic distribution of the cumulative sums as Brownian motion. The performance of the test is evaluated for simulated data from linear, bilinear and self-exciting…

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Confidence regions and tests for a change-point in a sequence of exponential family random variables

指数族独立随机变量序列的变点检验与置信区域

SUMMARY Maximum likelihood methods are used to test for a change in a sequence of independent exponential family random variables, with particular emphasis on the exponential distribution. The exact null and alternative distributions of the test statistics are found, and the power is compared with a test based on a linear trend statistic. Exact and approximate confidence regions for the change-point are based on the values accepted by a level x likelihood ratio test and a…

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On a Singularity in the Likelihood for a Change-Point Hazard Rate Model

变点风险率模型似然中的一个奇异性问题

A singularity identified by Nguyen, Rogers & Walker (1984) in the log likelihood function for a change-point hazard rate model is eliminated if the likelihood function is appropriately defined.

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Tests for Equality between Sets of Coefficients in Two Linear Regressions under Heteroscedasticity

异方差下两个线性回归系数集合相等的检验

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

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Aggregation, Structural Change, and Cross-Section Estimation

聚合、结构变化与截面估计

This article characterizes the local effects of parametric behavioral model change on relationships between aggregate variables, and it presents consistent estimators of such effects using cross-section data. Two equivalent interpretations of model-change effects are given: an “average-marginal” formulation and a cross-section regression formulation. The relation between model-change effects and maximum likelihood estimation of the behavioral parameters is explained.…

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Tests for Equality Between Sets of Coefficients in Two Linear Regressions Under Heteroscedasticity

异方差下两个线性回归系数集合的相等性检验

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

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A Diffusion Process and Its Applications to Detecting a Change in the Drift of Brownian Motion

扩散过程及其在检测布朗运动漂移变化中的应用

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…

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Asymptotic Score-Statistic Processes and Tests for Constant Hazard Against a Change-Point Alternative

渐近得分统计过程及恒定风险率对单变点备择的检验

The problem of testing for a constant failure rate against alternatives with failure rates involving a single change-point is considered. The asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an Ornstein-Uhlenbeck process. An example illustrates the methodology.

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Testing for Regression Coefficient Stability with a Stationary AR(1) Alternative

A bstract-We discuss the problem of testing for constant versus time varying regression coefficients. Our alternative hypothesis allows the coefficients to follow a stationary AR(1) process with unknown autoregressive parameter. Standard testing procedures are inappropriate since this parameter is identified only under the alternative. We propose a test statistic which is a function of a sequence of Score statistics, and depends only on the regressors and the OLS residuals.…

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Foreign-Exchange Rate Dynamics: An Empirical Study Using Maximum Entropy Spectral Analysis

外汇汇率动态:基于最大熵谱分析的实证研究

This study examines whether foreign-exchange rates evolve as a random walk by directly comparing the predictive ability of autoregressive (AR) models of spot rates with that of the random walk. To reduce the influence of model specifications on test results, we neither specify the order of the AR process a priori nor assume that the order is necessarily the same over the entire sample period. For each subperiod, the AR model is estimated by maximum entropy spectral analysis,…

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A Framework for Time Varying Parameter Regression Modeling

时变参数回归建模框架

A framework for time varying parameter regression models is developed and employed in modeling and forecasting price expectations, using the Livingston data. Alternative model formulations, which include various choices for both the stochastic processes generating the varying parameters and the sets of explanatory variables, are examined and compared by using this framework. These models, some of which have appeared elsewhere and some of which are new, are estimated and used…

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Optimal Detection of a Change in Distribution

分布变化的最优检测

Suppose one is able to observe sequentially a series of independent observations $X_1, X_2, \cdots$ such that $X_1, X_2, \cdots, X_{\nu-1}$ are iid distributed according to a known distribution $F_0$ and $X_\nu, X_{\nu+1}, \cdots$ are iid distributed according to a known distribution $F_1$. Assume that $\nu$ is unknown and the problem is to raise an alarm as soon as possible after the distribution changes from $F_0$ to $F_1$. Formally, the problem is to find a stopping rule $N$…

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Testing the Lucas Hypothesis on Output-Inflation Trade-offs

检验产出与通胀权衡中的卢卡斯假说

A Bayesian highest-posterior interval test that accounts for heteroscedasticity and for two regimes of autocorrelation is derived to test the Lucas variance hypothesis on output-inflation trade-offs. Japanese and U.S. data show that heteroscedasticity and autocorrelation tend to influence the test results. A Bayesian procedure and Akaike's information criterion are used to determine the order or autoregressive schemes, and a join point to partition the sample is estimated by…

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