Unknown Break Date Research Articles

Factor Selection and Structural Breaks

We develop a new approach to select risk factors in an asset pricing model that allows the set to change at multiple unknown break dates. Using the six factors displayed in Table 1 since 1963, we document a marked shift towards parsimonious models in the last two decades. Prior to 2005, five or six factors are selected, but just two are selected thereafter. This finding offers a simple implication for the factor zoo literature: ignoring breaks detects additional factors that are no longer relevant. Moreover, all omitted factors are priced by the selected factors in every regime. Finally, the selected factors outperform popular factor models as an investment strategy.

Testing for structural changes in large dimensional factor models via discrete Fourier transform

We propose a new test for structural changes in large dimensional factor models using a discrete Fourier transform (DFT) approach. When structural changes occur, the conventional principal component analysis may fail to estimate the common factors and factor loadings consistently, and the estimated residuals contain information about the structural changes. This allows us to compare the DFT of the estimated residuals weighted by the estimated common factors with the null (zero) spectrum implied by no structural change. The proposed test is powerful against both smooth structural changes and abrupt structural breaks with an unknown number of breaks and unknown break dates in factor loadings. It can detect a class of local alternatives at the rate N−1/2T−1/2, where N and T are the numbers of cross-sectional units and time periods, respectively. Monte Carlo studies demonstrate that the proposed test has reasonable size and excellent power in detecting various structural changes in factor loadings. When applied to the U.S. macroeconomic data, the test reveals significant and robust evidence of time-varying factor loadings for the post-Great Moderation sample and the pre-Great Recession subsample, which the existing literature may fail to address.

Asymptotic properties of Bayesian inference in linear regression with a structural break

This paper studies large sample properties of a Bayesian approach to inference about slope parameters γ in linear regression models with a structural break. In contrast to the conventional approach to inference about γ that does not take into account the uncertainty of the unknown break date, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein–von Mises type theorem (Bayesian asymptotic normality) for γ under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of γ to check robustness with respect to the uncertainty of the break date. Simulation studies show that the conventional confidence intervals of γ tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, we illustrate that the traditional confidence intervals on γ might underrepresent the true sampling uncertainty.

Likelihood ratio test for change in persistence

In this paper, we propose a likelihood ratio test for a change in persistence of a time series. We consider the null hypothesis of a constant persistence I(1) and an alternative in which the series changes from a stationary regime to a unit root regime or vice versa. Both known and unknown break dates are analyzed. Moreover, we consider a modification of a lag length selection procedure which provides better size control over various data generation processes. The bootstrap with recoloring also improves size. In general, our likelihood ratio-based tests show the best finite sample properties from all persistence change tests that use the null hypothesis of a unit root throughout.

Testing for parameter instability and structural change in persistent predictive regressions

This paper develops parameter instability and structural change tests within predictive regressions for economic systems governed by persistent vector autoregressive dynamics. Specifically, in a setting where all – or a subset – of the variables may be fractionally integrated and the predictive relation may feature cointegration, we provide sup-Wald break tests that are constructed using the Local speCtruM (LCM) approach. The new tests cover both parameter variation and multiple structural changes with unknown break dates, and the number of breaks being known or unknown. We establish asymptotic limit theory for the tests, showing that it coincides with standard testing procedures. As a consequence, existing critical values for tied-down Bessel processes may be applied, without modification. We implement the new structural change tests to explore the stability of the fractionally cointegrating relation between implied- and realized volatility (IV and RV). Moreover, we assess the relative efficiency of IV forecasts against a challenging time-series benchmark constructed from high-frequency data. Unlike existing studies, we find evidence that the IV–RV cointegrating relation is unstable, and that carefully constructed time-series forecasts are more efficient than IV in capturing low-frequency movements in RV.

Структурные сдвиги в моделях коинтеграции: многомерный случай

This review discusses methods of testing for a cointegration rank in a multivariate time series in the presence of structural breaks. The review covers both the methods with known and unknown break date. Multiple breaks are also considered. The issues of testing for cointegration with a possible change in the cointegration rank over time are discussed separately.

TESTING FOR STRUCTURAL CHANGES IN FACTOR MODELS VIA A NONPARAMETRIC REGRESSION

We propose a model-free test for structural changes in factor models. The basic idea is to regress the data on commonly estimated factors by local smoothing and compare the fitted values of time-varying factor loadings with those of time-invariant factor loadings estimated via principal component analysis. By construction, the test is designed to be powerful against both smooth structural changes and sudden structural breaks with a possibly unknown number of breaks and unknown break dates in the factor loadings. No restrictions on the form of alternatives or trimming of boundary regions near the beginning or end of the sample period is required for the test. The test has power to detect the usual nonparametric rate of local alternatives. Monte Carlo studies demonstrate excellent power of the test in detecting both smooth and sudden structural changes in the factor loadings. In an application using U.S. asset returns, we find significant evidence against time-invariant factor loadings.

The curvilinear relationship between environmental pollution and economic growth

PurposeThe genesis of Environmental Kuznets curve (EKC) of “grow now clean later” has led to a substantial deterioration of local as well as the global environment. India has not been spared of this malaise and accounts for the third-largest carbon dioxide emitter in the world. Thus, the present study revisits the curvilinear relationship between economic growth and environmental pollution in case of India over the period of 1971-2014.Design/methodology/approachDickey–Fuller generalised least square (DF-GLS) test developed by Elliott et al. is used to ensure that none of the variables is I(2). The study applies the autoregressive distributed lag (ARDL) bounds estimation technique to test for the existence of cointegration among variables and estimate long-run and short-run parameters. The study also applies the Bai–Perron structural break test with unknown break date to determine the threshold point. The study further uses the vector error correction model (VECM) Granger causality test to check the direction of causality between variables.FindingsThe ARDL bounds estimation technique confirms the cointegration among variables. The long-run coefficients of energy consumption, economic growth and financial development are found to have an adverse impact on environmental quality. The results also validate the existence of conventional EKC hypothesis. Bai–Perron structural break test, along with t-test and scatter graph, shows that inverted U-shaped relationship between environmental pollution and economic growth holds true. The VECM-based causality results support “growth hypothesis” both in the long run and short run.Research limitations/implicationsThis study refrained from considering a variety of variables, as the main intention of the study is to investigate whether any threshold or turnaround point exists for India. The future studies should consider a new set of variables (e.g. population, corruption index, social indicators, political scenario, energy research and development expenditures, foreign capital inflows, public investment towards alternate energy exploration, etc.) in the estimation of EKC hypothesis.Practical implicationsThe results validate the existence of conventional EKC hypothesis. Thereby the study argues that instead of being a threat to environmental quality, economic growth is observed to generate a sustainable environment to live in. Further, bi-directional causality is found between carbon emissions and economic growth. Thus, any effort to mitigate CO2 or environment conservation policy will impede economic growth. Consequently, controlling primary energy consumption and supply and replacing it with renewable and clean energy could be desirable for climate change mitigation.Originality/valueThe data set has been refined so that the EKC estimation issues raised by Stern (2004) are addressed. In particular, statistical properties of the data set such as serial correlation, presence of a stochastic or deterministic trend, has been adequately taken care of to remove any spurious correlation. Finally, various control variables have been included to provide consideration to issues of model adequacy, such as the possibility of omitted variables bias. To the authors’ best knowledge, there is no India-specific study which has taken care of data-related issues, as suggested by Stern, in the estimation of a curvilinear relationship between environmental degradation and economic growth in India. Further, this is the first study which has used Bai–Perron structural break test with unknown break date to identify the threshold point while estimating EKC in India.

Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions

This paper develops parameter instability and structural change tests within predictive regressions for economic systems governed by persistent vector autoregressive dynamics. Specifically, in a setting where all – or a subset – of the variables may be fractionally integrated and the predictive relation may feature cointegration, we provide sup-Wald break tests that are constructed using the Local speCtruM (LCM) approach. The new tests cover both parameter variation and multiple structural changes with unknown break dates, and the number of breaks being known or unknown. We establish asymptotic limit theory for the tests, showing that it coincides with standard testing procedures. As a consequence, existing critical values for tied-down Bessel processes may be applied, without modification. We implement the new structural change tests to explore the stability of the fractionally cointegrating relation between implied- and realized volatility (IV and RV). Moreover, we assess the relative efficiency of IV forecasts against a challenging time-series benchmark constructed from high-frequency data. Unlike existing studies, we find evidence that the IV-RV cointegrating relation is unstable, and that carefully constructed time-series forecasts are more efficient than IV in capturing low-frequency movements in RV. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Estimating and Testing for Multiple Distributional Structural Breaks via a Characteristic Function Approach

We estimate and test for multiple structural breaks in distribution with unknown break dates via a characteristic function approach. By minimizing the sum of squared generalized residuals, we can consistently estimate the break fractions. We propose a sup-F type test for structural breaks in distribution and suggest an information criterion and a sequential testing procedure to determine the number of breaks. We further construct a class of derivative tests to gauge the possible source of structural breaks, which is asymptotically more powerful than the nonparametric-based tests for structural breaks. Simulation studies show that our method performs well in determining the appropriate number of breaks and estimating the unknown breaks. Furthermore, the proposed tests have reasonable size and excellent power. In an application to exchange rate returns, our tests are able to detect structural breaks in distribution and locate the break dates. Our derivate tests indicate that the documented breaks appear to occur in variance and higher order moments, but not so often in mean.

Testing for Structural Changes in Large Dimensional Factor Models via Discrete Fourier Transform

We propose a new test for structural changes in large dimensional factor models via a discrete Fourier transform (DFT) approach. If structural changes occur, the conventional principal component analysis fails to estimate common factors and factor loadings consistently. The estimated residuals will contain information about structural changes. Therefore, we can compare the DFT of the estimated residuals with the null (zero) spectrum implied by no structural change. The proposed test is powerful against both smooth structural changes and abrupt structural breaks with a possibly unknown number of breaks and unknown break dates in factor loadings. It can detect a class of local alternatives at the parametric rate. As a result, the test is asymptotically more efficient than the existing tests in the factor model literature. And our test is also robust to serial and cross-sectional dependence of unknown form without having to estimate any long-run variance-covariance matrix. Moreover, it is easy to implement and tuning parameter-free. Monte Carlo studies demonstrate its reasonable size and excellent power in detecting various forms of structural changes in factor loadings. In an application to the U.S. macroeconomic data, we find significant and robust evidence of time-varying factor loadings.

Unstable Diffusion Indexes: With an Application to Bond Risk Premia

AbstractThis paper studies the empirically relevant problem of estimation and inference in diffusion index forecasting models with structural instability. Factor model and factor augmented regression both experience a structural change with different unknown break dates. In the factor model, we estimate factors and loadings by principal components. We consider least squares estimation of the factor augmented regression and propose a break test. The empirical application uncovers instabilities in the linkages between bond risk premia and macroeconomic factors.

Combining p-values to test for multiple structural breaks in cointegrated regressions

We propose a multiple hypothesis testing approach to assess structural stability in cointegrating regressions. Underlying tests are constructed via a Vector Error Correction Model and generalize the reduced rank regression procedures of Hansen (2003). We generalize the likelihood ratio test proposed in Hansen (2003) to accommodate unknown break dates through the specification of several scenarios regarding the number and the location of the breaks. We define a combined p-value adjustment, which proceeds by simulating the entire dataset imposing the relevant null hypothesis. This framework accounts for both correlation of underlying tests and the fact that empirically, parameters of interest often pertain to limited even though uncertain stylized-fact based change points. We prove asymptotic validity of the proposed procedure. Monte Carlo simulations show that proposed tests perform well in finite samples and circumvent Bonferroni-type adjustments. An application to the S&P 500 prices and dividends series illustrates the empirical validity of the proposed procedure.

A model-free consistent test for structural change in regression possibly with endogeneity

Structural instability leads to misleading inference and imprecise prediction of time series models that assume stationarity. We propose a model-free consistent test for structural change in regression by testing the instability of the Fourier transform of data. This novel approach avoids smoothed nonparametric estimation of the unknown regression function and so is free of the “curse of dimensionality” problem. Unlike the existing literature, we allow for endogenous and discrete regressors. By using a proper choice of weighting functions for the transform parameters in the Fourier transform, we avoid numerical integration so that our test statistic is easy to compute. Our test statistic has a convenient asymptotic N(0,1) distribution under the null hypothesis of no structural change and is consistent against a large class of smooth structural changes as well as abrupt structural breaks with unknown break dates. A Monte Carlo study and an empirical application show that our test performs reasonably well in finite samples.

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

SummaryMethodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous estimators based on functional principal component analysis are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the procedures proposed.

Unstable Diffusion Indexes: With an Application to Bond Risk Premia

This paper studies estimation and inference in diffusion indexes with structural instability. Factor model and factor augmented regression both experience a structural change with different unknown break dates. In the factor model, we estimate factors and loadings by principal components, and break fraction by concentrated least squares: convergence rates of the estimators are obtained, and model selection criteria robust to the unknown break date are introduced. We consider least squares estimation of the factor augmented regression and propose a break test. The empirical application uncovers potential instabilities in the linkages between bond risk premia and macroeconomic factors.

Do execution moratoriums increase homicide? Re-examining evidence from Illinois

This article revisits the event study by Cloninger and Marchesini (2006), who find that the declaration of the Illinois’ death penalty moratorium on 31 January 2000 had a homicide-promoting effect and resulted in 150 additional homicides over the period 2000–2003. We reassess the author’s identification strategy, which they refer to as ‘portfolio approach’ and which draws upon event studies in finance research. We argue that their methodology is not applicable in crime studies. Instead, we apply univariate time-series methods to test for a structural break at a known and unknown break date. We allow for unknown break points as the structural break might have occurred slightly earlier (criminals might have anticipated the moratorium) or later (due to persistence in criminal behaviour). In addition, we implement the synthetic control estimator which approximates the counterfactual homicide series by a weighted average of homicide outcomes in other US states. Based on various testing methods and two distinct data sets, we conclude that there is no empirical evidence to support the hypothesis that the Illinois’ execution moratorium significantly increased homicides.

Forecasting a long memory process subject to structural breaks

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model can be explained, from an econometric perspective, by our theoretical and simulation results.

Forecasting a Long Memory Process Subject to Structural Breaks

We develop an easy-to-implement method for forecasting a stationary auto-regressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an auto-regressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model is explained, from an econometric perspective, by our theoretical and simulation results.

Testing for Structural Change in Heterogeneous Panels with an Application to the Euro's Trade Effect

AbstractThis paper presents a structural change test for panel data models in which the break (or the change) affects some, but not all, cross-section units in the panel. The test is robust to non-normal, heteroskedastic and autocorrelated errors, as well as end-of-sample structural change. The test amounts to computing and comparing pre- and post-break sample statistics as Chow (1960) type F statistics averaged over cross-section units. The cases of known and unknown break date are both considered. Under mild assumptions, the test has a limiting standard normal distribution as the number of cross-sections tends to infinity. Monte Carlo experiments show that the test has good size and power under a wide range of circumstances, including when the break date is unknown and differs across individual units, and when errors exhibit cross-section dependence. Finally, the test is illustrated by seeking a break in the dynamics of trade among euro area countries following the introduction of the euro.