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Open AccessEditorial

Unit Roots and Structural Breaks

by Pierre Perron

Econometrics 2017, 5(2), 22; https://doi.org/10.3390/econometrics5020022 - 30 May 2017

Cited by 7 | Viewed by 9512

Abstract

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

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

Research

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280 KiB

Open AccessArticle

Selecting the Lag Length for the M^GLS Unit Root Tests with Structural Change: A Warning Note for Practitioners Based on Simulations

by Ricardo Quineche and Gabriel Rodríguez

Econometrics 2017, 5(2), 17; https://doi.org/10.3390/econometrics5020017 - 16 Apr 2017

Cited by 3 | Viewed by 7941

Abstract

This is a simulation-based warning note for practitioners who use the

M^{G L S}

unit root tests in the context of structural change using different selection lag length criteria. With

T = 100

, we find severe oversize problems when using some [...] Read more.

This is a simulation-based warning note for practitioners who use the

M^{G L S}

unit root tests in the context of structural change using different selection lag length criteria. With

T = 100

, we find severe oversize problems when using some criteria, while other criteria produce an undersizing behavior. In view of this dilemma, we do not recommend using these tests. While such behavior tends to disappear when

T = 250

, it is important to note that most empirical applications use smaller sample sizes such as

T = 100

or

T = 150

. The

A D F^{G L S}

test does not present an oversizing or undersizing problem. The only disadvantage of the

A D F^{G L S}

test arises in the presence of

M A (1)

negative correlation, in which case the

M^{G L S}

tests are preferable, but in all other cases they are very undersized. When there is a break in the series, selecting the breakpoint using the Supremum method greatly improves the results relative to the Infimum method. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

290 KiB

Open AccessArticle

Testing for a Structural Break in a Spatial Panel Model

by Aparna Sengupta

Econometrics 2017, 5(1), 12; https://doi.org/10.3390/econometrics5010012 - 6 Mar 2017

Cited by 8 | Viewed by 8245

Abstract

We consider the problem of testing for a structural break in the spatial lag parameter in a panel model (spatial autoregressive). We propose a likelihood ratio test of the null hypothesis of no break against the alternative hypothesis of a single break. The [...] Read more.

We consider the problem of testing for a structural break in the spatial lag parameter in a panel model (spatial autoregressive). We propose a likelihood ratio test of the null hypothesis of no break against the alternative hypothesis of a single break. The limiting distribution of the test is derived under the null when both the number of individual units N and the number of time periods T is large or N is ﬁxed and T is large. The asymptotic critical values of the test statistic can be obtained analytically. We also propose a break-date estimator that can be employed to determine the location of the break point following evidence against the null hypothesis. We present Monte Carlo evidence to show that the proposed procedure performs well in ﬁnite samples. Finally, we consider an empirical application of the test on budget spillovers and interdependence in ﬁscal policy within the U.S. states. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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488 KiB

Open AccessArticle

Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries

by Jesús Clemente, María Dolores Gadea, Antonio Montañés and Marcelo Reyes

Econometrics 2017, 5(1), 11; https://doi.org/10.3390/econometrics5010011 - 17 Feb 2017

Cited by 14 | Viewed by 9999

Abstract

This study reconsiders the common unit root/co-integration approach to test for the Fisher effect for the economies of the G7 countries. We first show that nominal interest and inflation rates are better represented as I(0) variables. Later, we use the Bai–Perron procedure to [...] Read more.

This study reconsiders the common unit root/co-integration approach to test for the Fisher effect for the economies of the G7 countries. We first show that nominal interest and inflation rates are better represented as I(0) variables. Later, we use the Bai–Perron procedure to show the existence of structural changes in the Fisher equation. After considering these breaks, we find very limited evidence of a total Fisher effect as the transmission coefficient of the expected inflation rates to nominal interest rates is very different than one. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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477 KiB

Open AccessArticle

Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses

by Seong Yeon Chang and Pierre Perron

Econometrics 2017, 5(1), 5; https://doi.org/10.3390/econometrics5010005 - 8 Jan 2017

Cited by 11 | Viewed by 8416

Abstract

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 [...] Read more.

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 trend with or without a concurrent level shift under both the null and alternative hypotheses. We show that the limit distribution of the proposed LM tests is standard normal. Finite sample simulation experiments show that the tests have good size and power. As an empirical analysis, we apply the tests to the Consumer Price Indices of the G7 countries. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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3266 KiB

Open AccessArticle

Consistency of Trend Break Point Estimator with Underspecified Break Number

by Jingjing Yang

Econometrics 2017, 5(1), 4; https://doi.org/10.3390/econometrics5010004 - 5 Jan 2017

Cited by 4 | Viewed by 8004

Abstract

This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such [...] Read more.

This paper discusses the consistency of trend break point estimators when the number of breaks is underspecified. The consistency of break point estimators in a simple location model with level shifts has been well documented by researchers under various settings, including extensions such as allowing a time trend in the model. Despite the consistency of break point estimators of level shifts, there are few papers on the consistency of trend shift break point estimators in the presence of an underspecified break number. The simulation study and asymptotic analysis in this paper show that the trend shift break point estimator does not converge to the true break points when the break number is underspecified. In the case of two trend shifts, the inconsistency problem worsens if the magnitudes of the breaks are similar and the breaks are either both positive or both negative. The limiting distribution for the trend break point estimator is developed and closely approximates the finite sample performance. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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397 KiB

Open AccessArticle

Fixed-b Inference for Testing Structural Change in a Time Series Regression

by Cheol-Keun Cho and Timothy J. Vogelsang

Econometrics 2017, 5(1), 2; https://doi.org/10.3390/econometrics5010002 - 30 Dec 2016

Cited by 6 | Viewed by 7847

Abstract

This paper addresses tests for structural change in a weakly dependent time series regression. The cases of full structural change and partial structural change are considered. Heteroskedasticity-autocorrelation (HAC) robust Wald tests based on nonparametric covariance matrix estimators are explored. Fixed-b theory is [...] Read more.

This paper addresses tests for structural change in a weakly dependent time series regression. The cases of full structural change and partial structural change are considered. Heteroskedasticity-autocorrelation (HAC) robust Wald tests based on nonparametric covariance matrix estimators are explored. Fixed-b theory is developed for the HAC estimators which allows fixed-b approximations for the test statistics. For the case of the break date being known, the fixed-b limits of the statistics depend on the break fraction and the bandwidth tuning parameter as well as on the kernel. When the break date is unknown, supremum, mean and exponential Wald statistics are commonly used for testing the presence of the structural break. Fixed-b limits of these statistics are obtained and critical values are tabulated. A simulation study compares the finite sample properties of existing tests and proposed tests. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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265 KiB

Open AccessArticle

Testing for the Equality of Integration Orders of Multiple Series

by Man Wang and Ngai Hang Chan

Econometrics 2016, 4(4), 49; https://doi.org/10.3390/econometrics4040049 - 15 Dec 2016

Cited by 1 | Viewed by 6677

Abstract

Testing for the equality of integration orders is an important topic in time series analysis because it constitutes an essential step in testing for (fractional) cointegration in the bivariate case. For the multivariate case, there are several versions of cointegration, and the version [...] Read more.

Testing for the equality of integration orders is an important topic in time series analysis because it constitutes an essential step in testing for (fractional) cointegration in the bivariate case. For the multivariate case, there are several versions of cointegration, and the version given in Robinson and Yajima (2002) has received much attention. In this definition, a time series vector is partitioned into several sub-vectors, and the elements in each sub-vector have the same integration order. Furthermore, this time series vector is said to be cointegrated if there exists a cointegration in any of the sub-vectors. Under such a circumstance, testing for the equality of integration orders constitutes an important problem. However, for multivariate fractionally integrated series, most tests focus on stationary and invertible series and become invalid under the presence of cointegration. Hualde (2013) overcomes these difficulties with a residual-based test for a bivariate time series. For the multivariate case, one possible extension of this test involves testing for an array of bivariate series, which becomes computationally challenging as the dimension of the time series increases. In this paper, a one-step residual-based test is proposed to deal with the multivariate case that overcomes the computational issue. Under certain regularity conditions, the test statistic has an asymptotic standard normal distribution under the null hypothesis of equal integration orders and diverges to infinity under the alternative. As reported in a Monte Carlo experiment, the proposed test possesses satisfactory sizes and powers. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

440 KiB

Open AccessArticle

Oil Price and Economic Growth: A Long Story?

by María Dolores Gadea, Ana Gómez-Loscos and Antonio Montañés

Econometrics 2016, 4(4), 41; https://doi.org/10.3390/econometrics4040041 - 28 Oct 2016

Cited by 18 | Viewed by 13100

Abstract

This study investigates changes in the relationship between oil prices and the US economy from a long-term perspective. Although neither of the two series (oil price and GDP growth rates) presents structural breaks in mean, we identify different volatility periods in both of [...] Read more.

This study investigates changes in the relationship between oil prices and the US economy from a long-term perspective. Although neither of the two series (oil price and GDP growth rates) presents structural breaks in mean, we identify different volatility periods in both of them, separately. From a multivariate perspective, we do not observe a significant effect between changes in oil prices and GDP growth when considering the full period. However, we find a significant relationship in some subperiods by carrying out a rolling analysis and by investigating the presence of structural breaks in the multivariate framework. Finally, we obtain evidence, by means of a time-varying VAR, that the impact of the oil price shock on GDP growth has declined over time. We also observe that the negative effect is greater at the time of large oil price increases, supporting previous evidence of nonlinearity in the relationship. Full article

(This article belongs to the Special Issue Unit Roots and Structural Breaks)

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