Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

Perron, Pierre; Yamamoto, Yohei

doi:10.3390/econometrics7020022

Cited by 12 publications

(9 citation statements)

References 12 publications

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“…Recently, Perron and Zhou (2008) and Zhou and Perron (2008) proposed a comprehensive procedure for testing jointly for possible multiple structural breaks in both mean and variance, and they employed this new method to reinvestigate the 22 macroeconomic variables used by Stock and Watson (2002) Somewhat surprisingly, they uncovered strong evidence indicating that there are two breaks in variance in many important US macroeconomic variables including GDP, inflation and the interest rate. Since all 22 variables have been appropriately transformed to eliminate trends and/or unit roots, these findings have important implications for the unit root test on the corresponding variables.…”

Section: Introductionmentioning

confidence: 96%

Unit Root Tests in the Presence of Multiple Breaks in Variance

Jeong

Kim

et al. 2017

Singapore Econ. Rev.

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Spurious rejections of the standard Dickey-Fuller (DF) test caused by a single variance break have been reported and some solutions to correct the problem have been proposed in the literature. Kim et al. (2002) put forward a correctly-sized unit root test robust to a single variance break, called the KLN test. However, there can be more than one break in variance in time series data as documented in Zhou and Perron (2008), so allowing only one break can be too restrictive. In this paper, we show that multiple breaks in variance can generate spurious rejections not only by the standard DF test but also by the KLN test. We then propose a bootstrap-based unit root test that is correctly-sized in the presence of multiple breaks in variance. Simulation experiments demonstrate that the proposed test performs well regardless of the number of breaks and the location of the breaks in innovation variance.

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Section: Introductionmentioning

confidence: 96%

Unit Root Tests in the Presence of Multiple Breaks in Variance

Jeong

Kim

et al. 2017

Singapore Econ. Rev.

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“…However, when a change in the conditional mean caused by some parameter change occurs, the residuals assuming the null hypothesis may be a poor approximation to the true errors. Hence, power issues become a concern; see Pitarakis (2004) and Perron and Yamamoto (2019) who investigated the power problem when structural changes are present both in the coefficients and in the error variance but either ones are neglected; see also Hansen (2000).…”

Section: Introductionmentioning

confidence: 99%

Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods

Perron

Yamamoto

2021

Journal Time Series Analysis

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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: first estimate the residuals assuming no changes in the regression coefficients; second, use the residuals to approximate the heteroskedastic asymptotic distribution or take an entire sample average to construct a test for which the variance process is averaged out. An alternative approach was proposed by Perron et al. (Perron et al. (2020). Quantitative Economics 11: 1019-1057) who provided a test for changes in the coefficients allowing for changes in the variance of the error term. We show that it transforms the variance profile into one that effectively has very little impact on the size of the test. With respect to the power properties, the two-steps procedures can suffer from non-monotonic power problems in dynamic models and in static models with a correction for serial correlation in the error. Most have power equals to size with zero-mean regressors. Even when the two-steps tests have power, it is generally lower than that of the latter test.

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“…shows that standard structural change tests do not have the correct size with nonstationary variance. Pitarakis (2004), Perron and Yamamoto (2019) and Xu (2015) document the extent of size distortions and power losses for various tests. Perron, Yamamoto and Zhou (2020) develop likelihood ratio tests of the joint hypothesis of changes in coe¢ cients and error variance in a linear regression model.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

Kejriwal

Perron³

2020

Journal Time Series Analysis

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This paper proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by nonstationary 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 either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime-speci…c bootstrap p-values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the …nite sample improvements o¤ered by our methods. An application to OECD in ‡ation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures.

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Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

Cited by 12 publications

References 12 publications

Unit Root Tests in the Presence of Multiple Breaks in Variance

Unit Root Tests in the Presence of Multiple Breaks in Variance

Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods

Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

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