Estimating and Testing Structural Changes in Multivariate Regressions

This paper considers issues related to estimation, inference, and computation with multiple structural changes that occur at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks that occur in all equations, breaks that occur in a subset of equations, and so forth. The method of estimation is quasi‐maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. For computation, an algorithm for an efficient procedure is proposed to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.     

我国通货膨胀率动态波动路径的结构性转变特征与统计检验

本文运用参数稳定性检验方法研究我国通货膨胀率的动态变化路径,发现我国通货膨胀率序列具有明显的结构转变特征;利用包含结构转变点的最小二乘估计方法,获得了我国通货膨胀率的结构转变点估计和区间估计;结合我国宏观经济运行事实,分析并刻画了具有结构转变特征的通货膨胀率动态过程,准确地给出自1984年以来的两次高通货膨胀区间.     

具有平滑迁移的ARFIMA模型及其应用

本文基于描述长记忆性的ARFIMA模型和具有结构性转变的平滑迁移模型,提出了联合检验两种时间序列性质的STARFIMA模型,并给出了估计模型系数的估计方法和检验非线性的刀切似然比方法.应用我国通货膨胀率的时间序列数据,我们应用Logistic型STARFIMA模型进行经验分析时发现,STARFIMA模型具有比ARFIMA模型更好的模拟效果和精度,而且该模型分别捕捉到了以通货膨胀率自身和加速通货膨胀率为转移变量的结构性转变,并发现在引入结构转变之后的通货膨胀率序列的记忆性变强的特征.     

A Methodology for Determining Interactions in Probabilistic Safety Assessment Models by Varying One Parameter at a Time

In risk analysis problems, the decision‐making process is supported by the utilization of quantitative models. Assessing the relevance of interactions is an essential information in the interpretation of model results. By such knowledge, analysts and decisionmakers are able to understand whether risk is apportioned by individual factor contributions or by their joint action. However, models are oftentimes large, requiring a high number of input parameters, and complex, with individual model runs being time consuming. Computational complexity leads analysts to utilize one‐parameter‐at‐a‐time sensitivity methods, which prevent one from assessing interactions. In this work, we illustrate a methodology to quantify interactions in probabilistic safety assessment (PSA) models by varying one parameter at a time. The method is based on a property of the functional ANOVA decomposition of a finite change that allows to exactly determine the relevance of factors when considered individually or together with their interactions with all other factors. A set of test cases illustrates the technique. We apply the methodology to the analysis of the core damage frequency of the large loss of coolant accident of a nuclear reactor. Numerical results reveal the nonadditive model structure, allow to quantify the relevance of interactions, and to identify the direction of change (increase or decrease in risk) implied by individual factor variations and by their cooperation.     

Testing the Time‐Variancy of Explanatory Factors of Strategic Change1

The article proposes an empirical framework able to: (1) assess the relative validity of both adaptive and inertial views of strategic change and (2) verify the potential time‐ or context‐dependency by testing the structural stability of the empirical model, in Spanish banks, 1983–1997. Results offer inconclusive findings regarding (1) but strong evidence to answer (2). The assumption of structural stability is rejected and the effect of many explanatory factors considered in the empirical model varies over time as some factors show different effects and/or significance levels depending on the period considered. These findings suggest that explanatory models of strategic change should be viewed as ‘time‐’ or ‘context‐dependent’. The article provides a conceptual model in which alternative explanations operate in a sequential way. The results highlight, first, that inconclusive past findings about adaptive versus inertial views should be reviewed under this new evidence, and future empirical research must assure that its methods and interpretations are robust to potential structural breakdowns; and second, the limitations raised by the static approach offered by the available theories/models when approaching the dynamic and complex nature of strategic change. Theoretical developments and implications for managerial practice are suggested.     

Risk Sharing in Private Information Models With Asset Accumulation: Explaining the Excess Smoothness of Consumption

We study testable implications for the dynamics of consumption and income of models in which first‐best allocations are not achieved because of a moral hazard problem with hidden saving. We show that in this environment, agents typically achieve more insurance than that obtained under self‐insurance with a single asset. Consumption allocations exhibit “excess smoothness,” as found and defined by Campbell and Deaton (1989). We argue that excess smoothness, in this context, is equivalent to a violation of the intertemporal budget constraint considered in a Bewley economy (with a single asset). We also show parameterizations of our model in which we can obtain a closed‐form solution for the efficient insurance contract and where the excess smoothness parameter has a structural interpretation in terms of the severity of the moral hazard problem. We present tests of excess smoothness, applied to U.K. microdata and constructed using techniques proposed by Hansen, Roberds, and Sargent (1991) to test the intertemporal budget constraint. Our theoretical model leads us to interpret them as tests of the market structure faced by economic agents. We also construct a test based on the dynamics of the cross‐sectional variances of consumption and income that is, in a precise sense, complementary to that based on Hansen, Roberds, and Sargent (1991) and that allows us to estimate the same structural parameter. The results we report are consistent with the implications of the model and are internally coherent.     

时变参数模型的最优滚动窗宽选择标准及应用

宏观经济领域中存在严重的结构突变性,模型估计量的优劣对估计样本规模是敏感的。本文针对时变参数模型,建立了滚动窗宽选择标准,通过最小化估计量的近似二次损失函数及最大化各子样本估计量间的曼哈顿距离选择窗宽大小,权衡了模型估计量的准确性和时变性两个相悖目标。蒙特卡罗模拟实验表明,本文所提出的方法在各种结构突变情形下均适用,能够应用于线性关系和非线性关系的时变参数模型中,且均具有稳健性。将该方法应用于我国金融网络的结构突变识别过程,显著改善了传统窗宽选择方法的结果。     

Conditional Linear Combination Tests for Weakly Identified Models

We introduce the class of conditional linear combination tests, which reject null hypotheses concerning model parameters when a data‐dependent convex combination of two identification‐robust statistics is large. These tests control size under weak identification and have a number of optimality properties in a conditional problem. We show that the conditional likelihood ratio test of Moreira, 2003 is a conditional linear combination test in models with one endogenous regressor, and that the class of conditional linear combination tests is equivalent to a class of quasi‐conditional likelihood ratio tests. We suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter. These plug‐in tests perform well in simulation and have optimal power in many strongly identified models, thus allowing powerful identification‐robust inference in a wide range of linear and nonlinear models without sacrificing efficiency if identification is strong.     

Conditional Inference With a Functional Nuisance Parameter

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite‐dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasi‐likelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples.     

Forecasting industrial production using structural time series models

Industrial production data series are volatile and often also cyclical. Hence, univariate time series models which allow for these features are expected to generate relatively accurate forecasts of industrial production. A particular class of unobservable components models — structural time series models — is used to generate forecasts of Austrian and German industrial production. A widely applied ARIMA model is used as a baseline for comparison. The empirical results show that the basic structural model generates more accurate forecasts than the ARIMA model when accuracy is measured in terms of size of error or directional change; and that the basic structural model forecasts better than the structural model with a cyclical component included on the basis of numerical measures, and tracking error for month-to-month changes.     

End‐of‐Sample Instability Tests

This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small—possibly as small as one. The well‐known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations, n+m, is large. We generalize the F test to cover regression models with much more general error processes, regressors that are not strictly exogenous, and estimation by instrumental variables as well as least squares. In addition, we extend the F test to nonlinear models estimated by generalized method of moments and maximum likelihood. Asymptotic critical values that are valid as n→∞ with m fixed are provided using a subsampling‐like method. The results apply quite generally to processes that are strictly stationary and ergodic under the null hypothesis of no structural instability.     

基于马尔科夫切换模型的上证指数周收益率时间序列分析

本文先对上证指数收益率时间序列做非线性检测,再对时间序列进行结构性变化检测,发现上证指数收益序列既是非线性时间序列又有结构性变化;通过构建一个3状态,3阶滞后的异方差马尔可夫切换模型对1990年12月21日至2008年8月22日上证指数周收益率时间序列规律进行了实证分析,采用极大似然估计法对模型参数进行估计,识别出股市波动的三种主要的状态:慢涨、慢跌和快涨;实证结果表明马尔可夫切换模型能够比较有效的刻画股市波动的阶段性特征.     

A Geometric Approach to Nonlinear Econometric Models

Conventional tests for composite hypotheses in minimum distance models can be unreliable when the relationship between the structural and reduced‐form parameters is highly nonlinear. Such nonlinearity may arise for a variety of reasons, including weak identification. In this note, we begin by studying the problem of testing a “curved null” in a finite‐sample Gaussian model. Using the curvature of the model, we develop new finite‐sample bounds on the distribution of minimum‐distance statistics. These bounds allow us to construct tests for composite hypotheses which are uniformly asymptotically valid over a large class of data generating processes and structural models.     

跳跃风险、结构突变与原油期货价格波动预测

本文主要是为了检验原油期货市场是否存在明显的跳跃风险和结构突变,并重点调查这两个因素是否对原油期货价格波动有预测作用。在经典或前沿的HAR-RV、HAR-S-RV和PSlev模型中,本文同时考虑跳跃风险和结构突变因素,构建了HAR-RV-J-SB、HAR-S-RV-J-SB和PSlev-J-SB模型。接着,以WTI原油期货的5分钟高频交易数据作为实证样本,对以上模型进行实证分析。实证结果显示：原油期货市场存在明显的跳跃风险和结构突变现象;HAR-RV-J-SB、HAR-S-RV-J-SB和PSlev-J-SB模型对原油期货价格波动的样本外预测精度都明显高于与之相对应的HAR-RV、HAR-S-RV和PSlev模型,且其结果是稳健的。特别地,在HAR-C和LHAR-RV等其它现有HAR族模型中加入跳跃风险和结构突变因素,也能得到类似的结果。本文的研究表明跳跃风险和结构突变因素能显著提高现有绝大多数HAR族模型对原油期货价格的预测精度,所以在HAR族模型的构建中这两个因素不能被忽视。     

Estimation and Inference With Weak,Semi‐Strong,and Strong Identification

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi‐parametric estimators. The consistency/lack‐of‐consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification‐robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers, the results are applied to a number of other models.     

Efficient Semiparametric Estimation of the Fama–French Model and Extensions

This paper develops a new estimation procedure for characteristic‐based factor models of stock returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time‐varying weights and a set of univariate nonparametric functions relating security characteristic to the associated factor betas. We use a time‐series and cross‐sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic‐beta functions. By avoiding the curse of dimensionality, our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three‐factor Fama–French model, Carhart's four‐factor extension of it that adds a momentum factor, and a five‐factor extension that adds an own‐volatility factor. We find that momentum and own‐volatility factors are at least as important, if not more important, than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against a general alternative using a new nonparametric test.     

Modeling the Adenoma and Serrated Pathway to Colorectal CAncer (ASCCA)

Several colorectal cancer (CRC) screening models have been developed describing the progression of adenomas to CRC. Currently, there is increasing evidence that serrated lesions can also develop into CRC. It is not clear whether screening tests have the same test characteristics for serrated lesions as for adenomas, but lower sensitivities have been suggested. Models that ignore this type of colorectal lesions may provide overly optimistic predictions of the screen‐induced reduction in CRC incidence. To address this issue, we have developed the Adenoma and Serrated pathway to Colorectal CAncer (ASCCA) model that includes the adenoma‐carcinoma pathway and the serrated pathway to CRC as well as characteristics of colorectal lesions. The model structure and the calibration procedure are described in detail. Calibration resulted in 19 parameter sets for the adenoma‐carcinoma pathway and 13 for the serrated pathway that match the age‐ and sex‐specific adenoma and serrated lesion prevalence in the COlonoscopy versus COlonography Screening (COCOS) trial, Dutch CRC incidence and mortality rates, and a number of other intermediate outcomes concerning characteristics of colorectal lesions. As an example, we simulated outcomes for a biennial fecal immunochemical test screening program and a hypothetical one‐time colonoscopy screening program. Inclusion of the serrated pathway influenced the predicted effectiveness of screening when serrated lesions are associated with lower screening test sensitivity or when they are not removed. To our knowledge, this is the first model that explicitly includes the serrated pathway and characteristics of colorectal lesions. It is suitable for the evaluation of the (cost)effectiveness of potential screening strategies for CRC.     

Testing for Regime Switching

We analyze use of a quasi‐likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime‐switching context. This test exploits mixture properties implied by the regime‐switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance parameters identified only under the alternative, or approximations using derivatives higher than second order. We exploit recent advances by Andrews (2001) and contribute to the literature by extending the scope of mixture models, obtaining asymptotic null distributions different from those in the literature. We further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime‐switching tests. We compare the size and power of our statistics to other useful tests for regime switching via Monte Carlo methods and find relatively good performance. We apply our methods to reexamine the classic cartel study of Porter (1983) and reaffirm Porter's findings.     

Classic Dose‐Response and Time Postinoculation Models for Leptospira

Leptospirosis is a preeminent zoonotic disease concentrated in tropical areas, and prevalent in both industrialized and rural settings. Dose‐response models were generated from 22 data sets reported in 10 different studies. All of the selected studies used rodent subjects, primarily hamsters, with the predominant endpoint as mortality with the challenge strain administered intraperitoneally. Dose‐response models based on a single evaluation postinfection displayed median lethal dose (LD₅₀) estimates that ranged between 1 and 10⁷ leptospirae depending upon the strain's virulence and the period elapsed since the initial exposure inoculation. Twelve of the 22 data sets measured the number of affected subjects daily over an extended period, so dose‐response models with time‐dependent parameters were estimated. Pooling between data sets produced seven common dose‐response models and one time‐dependent model. These pooled common models had data sets with different test subject hosts, and between disparate leptospiral strains tested on identical hosts. Comparative modeling was done with parallel tests to test the effects of a single different variable of either strain or test host and quantify the difference by calculating a dose multiplication factor. Statistical pooling implies that the mechanistic processes of leptospirosis can be represented by the same dose‐response model for different experimental infection tests even though they may involve different host species, routes, and leptospiral strains, although the cause of this pathophysiological phenomenon has not yet been identified.     

Leveraging the Strengths of Choice Models and Neural Networks: A Multiproduct Comparative Analysis*

Choice models and neural networks are two approaches used in modeling selection decisions. Defining model performance as the out‐of‐sample prediction power of a model, we test two hypotheses: (i) choice models and neural network models are equal in performance, and (ii) hybrid models consisting of a combination of choice and neural network models perform better than each stand‐alone model. We perform statistical tests for two classes of linear and nonlinear hybrid models and compute the empirical integrated rank (EIR) indices to compare the overall performances of the models. We test the above hypotheses by using data for various brand and store choices for three consumer products. Extensive jackknifing and out‐of‐sample tests for four different model specifications are applied for increasing the external validity of the results. Our results show that using neural networks has a higher probability of resulting in a better performance. Our findings also indicate that hybrid models outperform stand‐alone models, in that using hybrid models guarantee overall results equal or better than the two stand‐alone models. The improvement is particularly significant in cases where neither of the two stand‐alone models is very accurate in prediction, indicating that the proposed hybrid models may capture aspects of predictive accuracy that neither stand‐alone model is capable of on their own. Our results are particularly important in brand management and customer relationship management, indicating that multiple technologies and mixture of technologies may yield more accurate and reliable outcomes than individual ones.