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In many forecast evaluation applications, standard tests as well as tests allowing for time-variation in relative forecast ability build on heteroskedasticity-and-autocorrelation consistent (HAC) covariance estimators. Yet, the finite-sample performance of these asymptotics is often poor. “Fixed- (Formula presented.) ” asymptotics, used to account for long-run variance estimation, improve finite-sample performance under homoskedasticity, but lose asymptotic pivotality under time-varying volatility. Moreover, loss of pivotality due to time-varying volatility is found in the standard HAC framework in certain cases as well. We prove a wild bootstrap implementation to restore asymptotically pivotal inference for the above and new CUSUM- and Cramér-von Mises-based tests in a fairly general setup, allowing for estimation uncertainty from either a rolling window or a recursive approach when fixed- (Formula presented.) asymptotics are adopted to achieve good finite-sample performance. We then investigate the (time-varying) performance of professional forecasters relative to naive no-change and model-based predictions in real-time. We exploit the Survey of Professional Forecasters (SPF) database and analyze nowcasts and forecasts at different horizons for output and inflation. We find that not accounting for time-varying volatility seriously affects outcomes of tests for equal forecast ability: wild bootstrap inference typically yields convincing evidence for advantages of the SPF, while tests using non-robust critical values provide remarkably less. Moreover, we find significant evidence for time-variation of relative forecast ability, the advantages of the SPF weakening considerably after the “Great Moderation.”. in press

In many forecast evaluation applications, standard tests (e.g., Diebold and Mariano, 1995) as well as tests allowing for time-variation in relative forecast ability (e.g., Giacomini and Rossi, 2010) build on heteroskedasticity-and-autocorrelation consistent (HAC) covariance estimators. Yet, the finite-sample performance of these asymptotics is often poor. "Fixed-b" asymptotics (Kiefer and Vogelsang, 2005), used to account for long-run variance estimation, improve finitesample performance under homoskedasticity, but lose asymptotic pivotality under time-varying volatility. Moreover, loss of pivotality due to time-varying volatility is found in the standard HAC framework in certain cases as well. We prove a wild bootstrap implementation to restore asymptotically pivotal inference for the above and new CUSUM- and Cramér-von Mises based tests in a fairly general setup, allowing for estimation uncertainty from either a rolling window or a recursive approach when fixed-b asymptotics are adopted to achieve good finite-sample performance. We then investigate the (time-varying) performance of professional forecasters relative to naive no-change and model-based predictions in real-time. We exploit the Survey of Professional Forecasters (SPF) database and analyze nowcasts and forecasts at different horizons for output and inflation. We find that not accounting for time-varying volatility seriously affects outcomes of tests for equal forecast ability: wild bootstrap inference typically yields convincing evidence for advantages of the SPF, while tests using non-robust critical values provide remarkably less. Moreover, we find significant evidence for time-variation of relative forecast ability, the advantages of the SPF weakening considerably after the "Great Moderation"., Discussion Paper / SFB823;6/2021

This article discusses cointegration tests for nonlinear cointegration in the presence of variance breaks in the errors. We build on approaches of Cavaliere and Taylor (2006, Journal of Time Series Analysis) for heteroskedastic cointegration tests and of Choi and Saikkonen (2010, Econometric Theory) for nonlinear cointegration tests. We propose a bootstrap test and prove its consistency. A Monte Carlo study shows the approach to have appealing finite sample properties and to work better than an approach using subresiduals. We provide an empirical application to the environmental Kuznets curves (EKC), finding that the cointegration tests do not reject the EKC hypothesis in most cases., Discussion Paper / SFB823;26/2020

Das Praxissemester ist ein integraler Bestandteil in allen Lehramtsstudiengängen in Nordrhein-Westfalen. Dieses wird von der universitären Seite begleitet durch Seminarmodule, in denen eigene forschungsbezogene Abschlussberichte verfasst werden sollen. An vielen Universitäten ist jedoch eine Methodenausbildung nicht fest verankert. Um diese Lücke zu schließen wurde an der Universität Duisburg-Essen ein vollständig Online-basierter Selbstlernkurs entworfen. Das Konzept dieses Kurses und die Auswertung der angefallenen Daten ist der Fokus dieses Posters.

The fixed-b asymptotic framework provides refinements in the use of heteroskedasticity and autocorrelation consistent variance estimators. The resulting limiting distributions of t-statistics are, however, not pivotal when the unconditional variance changes over time. Such time-varying volatility is an important issue for many financial and macroeconomic time series. To regain pivotal fixed-b inference under time-varying volatility, we discuss three alternative approaches. We (i) employ the wild bootstrap (Cavaliere and Taylor, 2008, ET), (ii) resort to time transformations (Cavaliere and Taylor, 2008, JTSA) and (iii) consider to select test statistics and asymptotics according to the outcome of a heteroscedasticity test, since small-b asymptotics deliver standard limiting distributions irrespective of the socalled variance profile of the series. We quantify the degree of size distortions from using the standard fixed-b approach assuming homoskedasticity and compare the effectiveness of the corrections via simulations. It turns out that the wild bootstrap approach is highly recommendable in terms of size and power. An application to testing for equal predictive ability using the Survey of Professional Forecasters illustrates the usefulness of the proposed corrections.

The fixed-b asymptotic framework provides refinements in the use of heteroskedasticity and autocorrelation consistent variance estimators. We show however that the fixed-b limiting distributions of t-statistics are not pivotal when the variance of the underlying data generating process changes over time. To regain pivotal fixed-b inference under such time heteroskedasticity, we discuss three alternative approaches. We employ (1) the wild bootstrap (Cavaliere and Taylor, 2008, ET), (2) resort to time transformations (Cavaliere and Taylor, 2008, JTSA) and (3) suggest to pick suitable the asymptotics according to the outcome of a heteroskedasticity test, since small-b asymptotics deliver standard limiting distributions irrespective of the so-called variance profile of the series. We quantify the degree of size distortions from using the standard fixed-b approach and compare the effectiveness of the corrections via simulations. We also provide an empirical application to excess returns.

While the limiting null distributions of cointegration tests are invariant to a certain amount of conditional heteroskedasticity as long as global homoskedasticity conditions are fulfilled, they are certainly affected when the innovations exhibit time-varying volatility. Worse yet, distortions from single units accumulate in panels, where one must anyway pay special attention to dependence among cross-sectional units, be it time-dependent or not. To obtain a panel cointegration test robust to both global heteroskedasticity and cross-unit dependence, we start by adapting the nonlinear instruments method proposed for the Dickey-Fuller test by Chang (J of Econometrics 110, 261--292) to an error-correction testing framework. We show that IV-based testing of the null of no error-correction in individual equations results in asymptotic standard normality of the test statistic as long as the t-type statistics are computed with White heteroskedasticity-consistent standard errors. Remarkably, the result holds even in the presence of endogenous regressors, irrespective of the number of integrated covariates, and for any variance profile. Furthermore, a test for the null of no cointegration---in effect, a joint test against no error correction in any equation of each unit---retains the nice properties of the univariate tests. In panels with fixed cross-sectional dimension, both types of test statistics from individual units are shown to be asymptotically independent even in the presence of correlation or cointegration across units, leading to a panel test statistic robust to cross-unit dependence and unconditional heteroskedasticity. The tests perform well in panels of usual dimensions with innovations exhibiting variance breaks and a factor structure.

We investigate the OLS-based estimator s2 of the disturbance variance in an error component linear panel regression model when the disturbances are homoskedastic, but spatially correlated. Although consistent (Song and Lee, Econ. Lett. 2008), s2 can be arbitrarily biased towards zero in finite samples., Discussion Paper / SFB 823;18/2010