Pierre Perron

Boston University | BU · Department of Economics

Consider a linear model y = X + u with u = (u 1 ; :::; u T) and u t a serially correlated linear process given by u t = P 1 j= h c j e t j for a sequence of innovations e t. Given a set of instruments Z, the "optimal GMM" estimator based on the moment condition E(Zu) = 0 is by far the most commonly used method to estimate such models. It can, howev...

We consider issues related to the effect of climate change on the persistence of (trend‐corrected) temperatures using global gridded data for both land and oceans. We first discuss how the presence of trends and additive noise affects inference about persistence. Ignoring a trend induces an upward bias, while not accounting for noise induces a down...

We study the Feasible Generalized Least-Squares (FGLS) estimation of the parameters of a linear regression model in the presence of heteroskedasticity of unknown form in the errors. We suggest a Lasso based procedure to estimate the skedastic function of the residuals. The advantage of using Lasso is that it can handle a large number of potential c...

We consider the derivation of data-dependent simultaneous bandwidths for double kernel heteroscedasticity and autocorrelation consistent (DK-HAC) estimators. In addition to the usual smoothing over lagged autocovariances for classical HAC estimators, the DK-HAC estimator also applies smoothing over the time direction. We obtain the optimal bandwidt...

Study of the frequency and magnitude of climate extremes as the world warms is of utmost importance, especially separating the influence of natural and anthropogenic forcing factors. Record-breaking temperature and precipitation events have been studied using event-attribution techniques. Here, we provide spatial and temporal observation-based anal...

We present a frequentist-based approach to forecast time series in the presence of in-sample and out-of-sample breaks in the parameters of the forecasting model. We …rst model the parameters as following a random level shift process, with the occurrence of a shift governed by a Bernoulli process. In order to have a structure so that changes in the...

We consider a linear regression model with serially correlated errors. It is well known that with exogenous regressors Generalized Least-Squares is more efficient than Ordinary Least-Squares (OLS). However, there are usually three main reasons advanced for adopting OLS instead of GLS. The first is that it is generally believed that OLS is valid whe...

We provide tests to perform inference on the coefficient of a linear trend assuming the noise to be a fractionally integrated process with memory parameter d∈(−0.5,1.5) excluding the boundary case 0.5 by applying a quasi-generalized least-squares procedure using d-differences of the data. Doing so, the asymptotic distribution of the ordinary least-...

We assess the empirical evidence about the great moderation using a comprehensive framework to test for multiple structural changes in the coefficients and in the variance of the error term of a linear regression model provided by Perron et al. (Quant Econ 11:1019–1057, 2020). We apply it to the US real GDP and its major components for the period 1...

We propose methods to estimate and conduct inference on conditional quantile processes for models with both nonparametric and (locally or globally) linear components. We derive their asymptotic properties, optimal bandwidths, and uniform confidence bands over quantiles allowing for robust bias correction. Our framework covers the sharp regression d...

Large cities account for a significant share of national population and wealth, and exert high pressure on local and regional resources, exacerbating socioenvironmental risks. The replacement of natural landscapes with higher heat capacity materials because of urbanization and anthropogenic waste heat are some of the factors contributing to local c...

There has been a recent upsurge of interest in testing for structural changes in heteroskedastic time series, as changes in the variance invalidate the asymptotic distribution of conventional structural change tests. Several tests have been proposed that are robust to general form of heteroskedastic errors. The most popular use a two‐steps approach...

This paper studies the problem of testing partial parameter stability in cointegrated regression models. The existing literature considers a variety of models depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structural change). We first show that t...

This paper develops change-point methods for the time-varying spectrum of a time series. We focus on time series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less smooth under the alternative. We provide a general theory for inference about the degree of smoothness of the spect...

We establish new mean-squared error (MSE) bounds for long-run variance (LRV) estimation, valid for both stationary and nonstationary sequences that are sharper than previously established. The key element to construct such bounds is to use restrictions onthe degree of nonstationarity. Unlike previous bounds, they show how nonstationarity influences...

We establish theoretical and analytical results about the low frequency contamination induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We show that for short memory nonstationarity data these estimates ex...

We consider the derivation of data-dependent simultaneous bandwidths for double kernel heteroskedasticity and autocorrelation consistent (DK-HAC) estimators. In addition to the usual smoothing over lagged autocovariances for classical HAC estimators, the DK-HAC estimator also applies smoothing over the time direction. We obtain the optimal bandwidt...

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998, Econometrica 66, 47–78). The GL estimator is defined by an integration rather than optimiza...

The attribution of climate change allows for the evaluation of the contribution of human drivers to observed warming. At the global and hemispheric scales, many physical and observation-based methods have shown a dominant anthropogenic signal, in contrast, regional attribution of climate change relies on physically based numerical climate models. H...

I consider a linear regression model with serially correlated errors. The prevailing view is that Ordinary Least Squares (OLS) is consistent under very general conditions and all that needs to be done is to correct the standard errors using some Heteroskedas-ticity and Autocorrelation Consistent (HAC) estimate of the limit covariance matrix. On the...

Due to various feedback processes called Arctic amplification, the high-latitudes’ response to increases in radiative forcing is much larger than elsewhere in the world, with a warming more than twice the global average. Since the 1990’s, this rapid warming of the Arctic was accompanied by no-warming or cooling over midlatitudes in the Northern Hem...

The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of temporal aggregation, we provide the link between the sp...

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2020a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimizati...

We provide a comprehensive treatment of the problem of testing jointly for structural change in both the regression coefficients and the variance of the errors in a single equation regression involving stationary regressors. Our frame-work is quite general in that we allow for general mixing-type regressors and the assumptions imposed on the errors...

This article proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by non‐stationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup‐Wald tests of the null hypothesis that the process is...

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2020a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimizati...

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N ] , and let T → ∞ with h ↓ 0 while keeping the time span N fixed. We impose very mild...

Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and rel...

Kejriwal and Perron (2010, KP) provided a comprehensive treatment for the problem of testing multiple structural changes in cointegrated regression models. A variety of models were considered depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structu...

We consider the issue of forecast failure (or breakdown) and propose methods to assess retrospectively whether a given forecasting model provides forecasts which show evidence of changes with respect to some loss function. We adapt the classical structural change tests to the forecast failure context. First, we recommend that all tests should be ca...

In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the vari...

What transpires from recent research is that temperatures and radiative forcing seem to be characterized by a linear trend with two changes in the rate of growth. The first occurs in the early 60s and indicates a very large increase in the rate of growth of both temperature and radiative forcing series. This was termed as the “onset of sustained gl...

In our study, we present a purely statistical observations‐based model‐free analysis that provides evidence about Granger causality (GC) from long‐lived radiative forcings (LLRFs) to the climate trend (CT). This relies on having locally ordered breaks in the slopes of the trend functions of LLRF and the CT, with the break for LLRF occurring before...

What transpires from recent research is that temperatures and radiative forcing seem to be characterized by a linear trend with two changes in the rate of growth. The first occurs in the early 60s and indicates a very large increase in the rate of growth of both temperature and radiative forcing series. This was termed as the "onset of sustained gl...

This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models. Substantial advances have been made to cover models at a level of generality that allow a host of interesting practical...

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2017a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. The procedure relies on a Laplace-type estimator defined...

Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and rel...

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regular...

This article offers an updated and extended attribution analysis based on recently published versions of temperature and forcing datasets. It shows that both temperature and radiative forcing variables can be best represented as trend stationary processes with structural changes occurring in the slope of their trend functions and that they share a...

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-cor...

This special issue deals with problems related to unit roots and structural change, and the interplay between the two.[...]

Because of low-frequency internal variability, the observed and underlying warming trends in temperature series can be markedly different. Important differences in the observed nonlinear trends in hemispheric temperature series suggest that the northern and southern hemispheres have responded differently to the changes in the radiative forcing. Usi...

What transpires from recent research is that temperatures and forcings seem to be characterized by a linear trend with two changes in the rate of growth. The …rst occurs in the early 60s and indicates a very large increase in the rate of growth of both temperatures and radiative forcings. This was termed as the " onset of sustained global warming "...

This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999), which are locally best invariant and uniformly most powerful, to allow for a slope change in tr...

Recent literature has shown that the volatility of exchange rate returns displays long memory features. It has also been shown that if a short memory process is contaminated by level shifts, the estimate of the long memory parameter tends to be upward biased. In this article, we directly estimate a random level shift model to the logarithm of the a...

This paper first generalizes the trend-cycle decomposition framework of Perron and Wada (2009) based on unobserved components models with innovations having a mixture of normals distribution, which is able to handle sudden level and slope changes to the trend function as well as outliers. We investigate how important are the differences in the impl...

We consider issues related to inference about locally ordered breaks in a system of equations, as originally proposed by Qu and Perron (2007). These apply when break dates in different equations within the system are not separated by a positive fraction of the sample size. This allows constructing joint confidence intervals of all such locally orde...

This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu (2009a) and is based on a...

We consider the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous, i.e., correlated with the errors. We show that even in the presence of endogenous regressors, it is still preferable to simply estimate the break dates and test for structural change using the usual ordinary leas...

This paper considers constructing con…dence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the per-formance of various procedures in terms of exact coverage rates and lengths of the con…dence intervals. These include the procedures of Bai (1997) based on the asymp-totic distribution...

Perron and Zhu (2005) established the consistency, rate of convergence, the limiting distri-butions of parameter estimates in a linear time trend with a change in slope with or without a concurrent change in level. They considered the dichotomous cases whereby the errors are short-memory, I(0), or have an autoregressive unit root, I(1). We extend t...

Giacomini and Rossi (2010) proposed a uctuations test and a one-time reversal test for comparing the out-of-sample forecasting performance of two competing models in the presence of possible instabilities. In the simulations and empirical applications, they use a version of their test based on the sample variance of the loss di¤erences instead of t...

We extend the random level shift (RLS) model of Lu and Perron (2010) to the volatility of asset prices, which consists of a short memory process and a random level shift component. Motivated by empirical features, (a) we specify a time-varying probability of shifts as a function of large negative lagged returns; and (b) we incorporate a mean revert...

The e¤ects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of temporal aggregation, we provide the link between the spe...

An ever-growing body of evidence regarding observed changes in the climate system has been gathered over the last three decades, and large modeling efforts have been carried to explore how climate may evolve during the present century. The impacts from both observed weather and climate endured during the twentieth century and the magnitude of the p...

The warming of the climate system is unequivocal as evidenced by an increase in global temperatures by 0.8 °C over the past century. However, the attribution of the observed warming to human activities remains less clear, particularly because of the apparent slow-down in warming since the late 1990s. Here we analyse radiative forcing and temperatur...

This paper considers methods for estimating and testing multiple structural changes occuring at unknown dates in linear models using band spectral regressions. We con- sider changes over time within some frequency bands, permitting the coefficients to be di¤erent across frequency bands. Using standard assumptions, we show that the limit distributio...

This paper proposes a framework for the modelling, inference and forecasting of volatility in the presence of level shifts of unknown timing, magnitude and frequency. First, we consider a stochastic volatility model comprising both a level shift and a short-memory component, with the former modelled as a compound binomial process and the latter as...

We study the finite sample properties of tests for structural changes in the trend function of a time series that do not require knowledge of the degree of persistence in the noise component. The tests of interest are the quasi-feasible generalized least squares procedure by Perron and Yabu (2009b) and the weighted average of the regression t-stati...

In this paper evidence of anthropogenic influence over the warming of the 20th century is presented and the debate regarding the time-series properties of global temperatures is addressed in depth. The 20th century global temperature simulations produced for the Intergovernmental Panel on Climate Change's Fourth Assessment Report and a set of the r...

Nonparametric nonlinear co-trending test for TRF, SOLAR, WM_GHG, and . (PDF)

ADF test on the residuals of the regressions of the ensemble average of global temperature simulations on: 1) TRF; 2) WM_GHG and; 3) SOLAR. (PDF)

Supplementary methods and results. (PDF)

Standard unit root tests applied to global temperature simulations and radiative forcing series. (PDF)

We provide a theoretical framework to explain the empirical finding that the estimated betas are sensitive to the sampling interval even when using continuously compounded returns. We suppose that stock prices have both permanent and transitory components. The discrete time representation of the beta depends on the sampling interval and two compone...

This paper studies issues related to the estimation of a structural change in the persistence of a univariate time series. The break is such that the process has a unit root [i.e., is I(1)] in the pre-break regime but reverts to a stationary [i.e., I(0)] process in the post-break regime or vice versa. T. T. L. Chong [Econom. Theory 17, No. 1, 87–15...

We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we c...

Roy, Falk and Fuller (2004) presented a procedure aimed at providing a test for the value of the slope of a trend function that has (nearly) controlled size in autoregressive models whether the noise component is stationary or has a unit root. In this note, we document errors in both their theoretical results and the simulations they reported. Once...

We analyze di¤erent residual-based tests for the null of no cointegration using GLS detrended data. We nd and simulate the limiting distributions of these statistics when GLS demeaned and GLS detrended data are used. The distributions depend of the number of right-hand side variables, the type of deterministic components used in the cointegration e...

Climate change detection and attribution have been the subject of intense research and debate over at least four decades. However, direct attribution of climate change to anthropogenic activities using observed climate and forcing variables through statistical methods has remained elusive, partly caused by the difficulties for correctly identifying...

We consider modeling and forecasting a variety of asset return volatility series by adding a random level shift component to the usual long-memory ARFIMA model. We propose a parametric state space model with an accompanying estimation and forecasting framework that combines long memory and level shifts by decomposing the underlying process into a s...

For more than two decades a debate regarding the time-series properties of global and hemispheric temperatures has taken place on the climate change literature and it has hardly been settled at the present time. This paper analyzes the IPCC's AR4 20c3m simulations using modern econometric techniques and provides new evidence to support that global...

We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts and de-terministic time trends. The estimators are simple trimmed versions of the popular log-periodogram regression estimator that employ certain sample size-dependent, and in some cases, data...

We consider the estimation of a random level shift model for which the series of interest is the sum of a short-memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a process which is 0 with some probability (1 − α) and is a r...

It has been argued that estimating the spectral density function of a stationary stochastic process at the zero frequency (or the so-called long-run variance) is an ill-posed problem so that any estimate will have an infinite minimax risk (e.g., Pötscher 2002). Most often it is a nuisance parameter that is present in the limit distribution of some...