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Pierre Perron

Boston University, Economics, Faculty Member

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Hong Kong Baptist University

Apostolos Serletis

University of Calgary

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Osmania University

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Dokuz Eylül University

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Papers by Pierre Perron

A Note on Johansen's Cointegration Procedure when Trends are Present

This note discusses some issues that arise when Johansen's (1991) framework is used to analyze co... more This note discusses some issues that arise when Johansen's (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We distinguish "stochastic" and "deterministic" cointegration, arguing that stochastic cointegration is sufTicient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen's (1991) method, which includes only a constant term in the estimated regression system, does not allow for stochastic cointegration. We propose to modify Johansen's method by including a vector of deterministic linear trends in the estimated modeL We present tabulated critical values of the maximal eigenvalue and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.

Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data

by Marcio Garcia, Regina Cati, and Pierre Perron

Journal of Applied Econometrics, 1999

This paper considers econometric issues related to time-series data that have been subject to abr... more This paper considers econometric issues related to time-series data that have been subject to abrupt governmental interventions. The motivating example for this study is the Brazilian monthly in¯ation rate (1974 : 1±1993 : 6) which we use throughout for illustration. This series has been heavily in¯uenced by the eect of so-called shock plans implemented by various governments starting in the mid-1980s. The plans act as`inliers' in the sense that the series is temporarily brought down to low levels before returning to its previous trend path. We analyse the eects on standard unit root tests and measures of persistence caused by the presence of these`inliers'. We show a substantial bias in favour of concluding that the series is stationary and that shocks have temporary eects. We then construct appropriately corrected statistics which take into account the presence of the plans. These show, unlike the standard tests, that the stochastic behaviour of the in¯ation rate was indeed unstable over this period. Simulation results are presented to support the adequacy of our corrected statistics.

Sampling Interval and estimated Betas : Implications for the Presence of Transitory Components in Stock Prices

by Cosme Vodounou and Pierre Perron

THE VARIANCE RATIO TEST: AN ANALYSIS OF SIZE AND POWER BASED ON A CONTINUOUS-TIME ASYMPTOTIC FRAMEWORK

by Cosme Vodounou and Pierre Perron

Econometric Theory, 2005

We consider the statistical properties of the variance ratio statistic in the context of testing ... more We consider the statistical properties of the variance ratio statistic in the context of testing for market efficiency defined by uncorrelated returns+ The statistic is then the ratio of the variance of K-period returns to the variance of one-period returns scaled by K+ We use a continuous-time asymptotic framework whereby we let the sample size increase to infinity keeping the span of the data fixed+ We also let the aggregation parameter K increase such that K0T r k as T, the sample size, increases to infinity+ We consider the limit of the statistic under the null hypothesis and under three alternative hypotheses that have been popular in the finance literature+ Our analysis permits us to address size and power issues with respect to k and the sampling interval used+ Our theoretical and simulation results show that power is initially increasing as k increases but then decreases with further increases in k+ This shows that for any given alternative there exists a value of K relative to T that will maximize power+ We thus investigate the properties of a test that is the maximal value of the variance ratio over a range of possible values for K+ The importance of the trimming to define this range is highlighted+ This paper is drawn from chapter 2 of Vodounou's Ph+D+ dissertation at the Université de Montréal~Vodounou, 1997!+ We thank two referees for useful comments and Tomoyoshi Yabu and Xiaokang Zhu for research assis-tance+ Perron acknowledges financial support from the Social Sciences and Humanities Research

Tests of return predictability: an analysis of their properties based on a continuous time asymptotic framework

by Cosme Vodounou and Pierre Perron

Journal of Empirical Finance, 2004

ABSTRACT We consider the statistical properties of tests for return predictability based on regre... more ABSTRACT We consider the statistical properties of tests for return predictability based on regressing returns or multi-period returns on some variable such as the dividend/price ratio. We use a continuous time asymptotic framework whereby we let the sample size increase to infinity keeping the span of the data fixed. The data generating process specifies that prices and dividends are a multivariate Ohrnstein–Uhlenbeck process which encompasses the null and alternative hypotheses that returns are uncorrelated or correlated with the dividend/price ratio. For the multi-period returns case, say K-periods, we let K/T→κ as in [Journal of Financial Economics 25 (1989) 323]. We derive the continuous time limit of the relevant t-statistic based on different estimates of the standard error of the estimate. Our analysis permits us to address size and power issues with respect to κ and the sampling interval used. Our theoretical and simulation results show that power is decreasing as κ increases, contrary to the theoretical result of [Journal of Empirical Finance 8 (2001) 459] based on the [Annals of Mathematical Statistics 31 (1960) 276] approximate slope analysis. Also, power depends much more on the span of the data than on the number of observations per se. The issue of size distortions for commonly used procedures is also addressed.

Asymptotic approximations in the near-integrated model with a non-zero initial condition

by Cosme Vodounou and Pierre Perron

Econometrics Journal, 2001

Sampling Interval and Estimated Betas: Implications for the Presence of Transitory Components in Stock Prices

by Cosme Vodounou and Pierre Perron

We provide a theoretical framework to explain the empirical finding that the estimated betas are ... more 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 components labelled "permanent and transitory betas". We show that if no transitory component is present in stock prices then no sampling interval effect occurs. However, the presence of a transitory component implies that the beta is an increasing (decreasing) function of the sampling interval for more (less) risky assets. In our framework, assets are labelled risky if their "permanent beta" is greater than their "transitory beta" and vice versa for less risky assets. Simulations show that our theoretical results provide good approximations for the estimated betas in small samples. We provide empirical evidence about the presence of negative serial correlation and mean reversion in the returns of the portfolios consider. We discuss why our model is better able to provide an explanation for this sampling interval effect than other models in the literature. * We wish to thank Xiaokang Zhu and Zhongjun Qu for help and comments on previous drafts. Perron acknowledges financial support form the Social Sciences and Humanities Research

Asymptotic Approximations in the Near-Integrated Model with a NonZero Initial Condition

by Cosme Vodounou and Pierre Perron

Residual Based Tests for Cointegration with GLS Detrended Data

by Gabriel Rodríguez and Pierre Perron

Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations

Journal of Econometrics, 2014

Trend, Unit Root and Structural Change in Macroeconomic Time Series

Cointegration, 1994

Inference on Locally Ordered Breaks in Multiple Regressions

Econometric Reviews, 2015

Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions

We consider the problem of estimating and testing for multiple breaks in a single equation framew... more 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. First, we show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable (IV) procedure involves regressors and errors that satisfy all the assumptions in so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, as well as the limit distributions of the tests, are obtained as simple consequences. More importantly from a practical perspective, 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 leastsquares (OLS) framework. In most cases, it delivers estimates of the break dates with higher precision and tests with higher power compared to those obtained using an IV method. To illustrate the relevance of our theoretical results, we consider the stability of the New Keynesian hybrid Phillips curve. IV-based methods do not indicate any instability. On the other hand, OLS-based ones strongly indicate a change in 1991:1 and that after this date the model looses all explanatory power. JEL Classification Number: C22.

The HUMP-shaped behavior of macroeconomic fluctuations

Empirical Economics, 1993

We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shoc... more We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shocks to macroeconomic variables (in particular real GNP) have effects that endure over an indefinite horizon. This conclusion is drawn from the presence of a unit root in the univariate time series representation. Following Perron (1989), we challenge this assessment arguing that most macroeconomic variables are better construed as stationary fluctuations around a breaking trend function. The trend function is linear in time except for a sudden change in its intercept in 1929 (The Great Crash) and a change in slope after 1973 (following the oil price shock). Using a measure of persistence suggested by Cochrane (1988) we find that shocks have small permanent effects, if any, To analyze the effects of shocks at finite horizon, we select a member of the ARMA(p, q) class applied to the appropriately detrended series. For the majority of the variables analyzed the implied weights of the moving-average representation have the once familiar humped shape.

Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors

We consider the problem of estimating and testing for multiple breaks in a single equation framew... more 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. First, we show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable (IV) procedure involves regressors and errors that satisfy all the assumptions in

Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]

Econometrica, Feb 1, 1993

If you experience problems downloading a file, check if you have the proper application to view i... more

The Exact Error in Estimating the Special Density at the Origin

Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties

Cahiers De Recherche, 1994

On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

considered the problem of testing for general types of parameter variations, including infrequent... more considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-calledqLL test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the sup-Wald test does not show this non-monotonicity and its power is far superior to thê qLL test when the break is not very small. We claim that the optimality of theqLL test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use fixed-break size asymptotic approximations to assess the relative efficiency or power of the two tests. When doing so, it is shown that the sup-Wald test indeed dominates theqLL test and, in many cases, the latter has zero relative asymptotic efficiency. JEL Classification Number: C22.

Estimating & Testing Linear Models with Multiple Structural Changes

A Note on Johansen's Cointegration Procedure when Trends are Present

This note discusses some issues that arise when Johansen's (1991) framework is used to analyze co... more This note discusses some issues that arise when Johansen's (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We distinguish "stochastic" and "deterministic" cointegration, arguing that stochastic cointegration is sufTicient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen's (1991) method, which includes only a constant term in the estimated regression system, does not allow for stochastic cointegration. We propose to modify Johansen's method by including a vector of deterministic linear trends in the estimated modeL We present tabulated critical values of the maximal eigenvalue and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.

Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data

by Marcio Garcia, Regina Cati, and Pierre Perron

Journal of Applied Econometrics, 1999

This paper considers econometric issues related to time-series data that have been subject to abr... more This paper considers econometric issues related to time-series data that have been subject to abrupt governmental interventions. The motivating example for this study is the Brazilian monthly in¯ation rate (1974 : 1±1993 : 6) which we use throughout for illustration. This series has been heavily in¯uenced by the eect of so-called shock plans implemented by various governments starting in the mid-1980s. The plans act as`inliers' in the sense that the series is temporarily brought down to low levels before returning to its previous trend path. We analyse the eects on standard unit root tests and measures of persistence caused by the presence of these`inliers'. We show a substantial bias in favour of concluding that the series is stationary and that shocks have temporary eects. We then construct appropriately corrected statistics which take into account the presence of the plans. These show, unlike the standard tests, that the stochastic behaviour of the in¯ation rate was indeed unstable over this period. Simulation results are presented to support the adequacy of our corrected statistics.

Sampling Interval and estimated Betas : Implications for the Presence of Transitory Components in Stock Prices

by Cosme Vodounou and Pierre Perron

THE VARIANCE RATIO TEST: AN ANALYSIS OF SIZE AND POWER BASED ON A CONTINUOUS-TIME ASYMPTOTIC FRAMEWORK

by Cosme Vodounou and Pierre Perron

Econometric Theory, 2005

We consider the statistical properties of the variance ratio statistic in the context of testing ... more We consider the statistical properties of the variance ratio statistic in the context of testing for market efficiency defined by uncorrelated returns+ The statistic is then the ratio of the variance of K-period returns to the variance of one-period returns scaled by K+ We use a continuous-time asymptotic framework whereby we let the sample size increase to infinity keeping the span of the data fixed+ We also let the aggregation parameter K increase such that K0T r k as T, the sample size, increases to infinity+ We consider the limit of the statistic under the null hypothesis and under three alternative hypotheses that have been popular in the finance literature+ Our analysis permits us to address size and power issues with respect to k and the sampling interval used+ Our theoretical and simulation results show that power is initially increasing as k increases but then decreases with further increases in k+ This shows that for any given alternative there exists a value of K relative to T that will maximize power+ We thus investigate the properties of a test that is the maximal value of the variance ratio over a range of possible values for K+ The importance of the trimming to define this range is highlighted+ This paper is drawn from chapter 2 of Vodounou's Ph+D+ dissertation at the Université de Montréal~Vodounou, 1997!+ We thank two referees for useful comments and Tomoyoshi Yabu and Xiaokang Zhu for research assis-tance+ Perron acknowledges financial support from the Social Sciences and Humanities Research

Tests of return predictability: an analysis of their properties based on a continuous time asymptotic framework

by Cosme Vodounou and Pierre Perron

Journal of Empirical Finance, 2004

ABSTRACT We consider the statistical properties of tests for return predictability based on regre... more ABSTRACT We consider the statistical properties of tests for return predictability based on regressing returns or multi-period returns on some variable such as the dividend/price ratio. We use a continuous time asymptotic framework whereby we let the sample size increase to infinity keeping the span of the data fixed. The data generating process specifies that prices and dividends are a multivariate Ohrnstein–Uhlenbeck process which encompasses the null and alternative hypotheses that returns are uncorrelated or correlated with the dividend/price ratio. For the multi-period returns case, say K-periods, we let K/T→κ as in [Journal of Financial Economics 25 (1989) 323]. We derive the continuous time limit of the relevant t-statistic based on different estimates of the standard error of the estimate. Our analysis permits us to address size and power issues with respect to κ and the sampling interval used. Our theoretical and simulation results show that power is decreasing as κ increases, contrary to the theoretical result of [Journal of Empirical Finance 8 (2001) 459] based on the [Annals of Mathematical Statistics 31 (1960) 276] approximate slope analysis. Also, power depends much more on the span of the data than on the number of observations per se. The issue of size distortions for commonly used procedures is also addressed.

Asymptotic approximations in the near-integrated model with a non-zero initial condition

by Cosme Vodounou and Pierre Perron

Econometrics Journal, 2001

Sampling Interval and Estimated Betas: Implications for the Presence of Transitory Components in Stock Prices

by Cosme Vodounou and Pierre Perron

We provide a theoretical framework to explain the empirical finding that the estimated betas are ... more 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 components labelled "permanent and transitory betas". We show that if no transitory component is present in stock prices then no sampling interval effect occurs. However, the presence of a transitory component implies that the beta is an increasing (decreasing) function of the sampling interval for more (less) risky assets. In our framework, assets are labelled risky if their "permanent beta" is greater than their "transitory beta" and vice versa for less risky assets. Simulations show that our theoretical results provide good approximations for the estimated betas in small samples. We provide empirical evidence about the presence of negative serial correlation and mean reversion in the returns of the portfolios consider. We discuss why our model is better able to provide an explanation for this sampling interval effect than other models in the literature. * We wish to thank Xiaokang Zhu and Zhongjun Qu for help and comments on previous drafts. Perron acknowledges financial support form the Social Sciences and Humanities Research

Asymptotic Approximations in the Near-Integrated Model with a NonZero Initial Condition

by Cosme Vodounou and Pierre Perron

Residual Based Tests for Cointegration with GLS Detrended Data

by Gabriel Rodríguez and Pierre Perron

Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations

Journal of Econometrics, 2014

Trend, Unit Root and Structural Change in Macroeconomic Time Series

Cointegration, 1994

Inference on Locally Ordered Breaks in Multiple Regressions

Econometric Reviews, 2015

Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions

We consider the problem of estimating and testing for multiple breaks in a single equation framew... more 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. First, we show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable (IV) procedure involves regressors and errors that satisfy all the assumptions in so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, as well as the limit distributions of the tests, are obtained as simple consequences. More importantly from a practical perspective, 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 leastsquares (OLS) framework. In most cases, it delivers estimates of the break dates with higher precision and tests with higher power compared to those obtained using an IV method. To illustrate the relevance of our theoretical results, we consider the stability of the New Keynesian hybrid Phillips curve. IV-based methods do not indicate any instability. On the other hand, OLS-based ones strongly indicate a change in 1991:1 and that after this date the model looses all explanatory power. JEL Classification Number: C22.

The HUMP-shaped behavior of macroeconomic fluctuations

Empirical Economics, 1993

We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shoc... more We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shocks to macroeconomic variables (in particular real GNP) have effects that endure over an indefinite horizon. This conclusion is drawn from the presence of a unit root in the univariate time series representation. Following Perron (1989), we challenge this assessment arguing that most macroeconomic variables are better construed as stationary fluctuations around a breaking trend function. The trend function is linear in time except for a sudden change in its intercept in 1929 (The Great Crash) and a change in slope after 1973 (following the oil price shock). Using a measure of persistence suggested by Cochrane (1988) we find that shocks have small permanent effects, if any, To analyze the effects of shocks at finite horizon, we select a member of the ARMA(p, q) class applied to the appropriately detrended series. For the majority of the variables analyzed the implied weights of the moving-average representation have the once familiar humped shape.

Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors

We consider the problem of estimating and testing for multiple breaks in a single equation framew... more 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. First, we show based on standard assumptions about the regressors, instruments and errors that the second stage regression of the instrumental variable (IV) procedure involves regressors and errors that satisfy all the assumptions in

Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]

Econometrica, Feb 1, 1993

If you experience problems downloading a file, check if you have the proper application to view i... more

The Exact Error in Estimating the Special Density at the Origin

Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties

Cahiers De Recherche, 1994

On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

considered the problem of testing for general types of parameter variations, including infrequent... more considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-calledqLL test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the sup-Wald test does not show this non-monotonicity and its power is far superior to thê qLL test when the break is not very small. We claim that the optimality of theqLL test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use fixed-break size asymptotic approximations to assess the relative efficiency or power of the two tests. When doing so, it is shown that the sup-Wald test indeed dominates theqLL test and, in many cases, the latter has zero relative asymptotic efficiency. JEL Classification Number: C22.

Estimating & Testing Linear Models with Multiple Structural Changes

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