Simple Robust Testing of Regression Hypotheses

Kiefer, Nicholas M.; Vogelsang, Timothy J.; Bunzel, Helle

doi:10.1111/1468-0262.00128

Cited by 230 publications

(205 citation statements)

References 10 publications

(12 reference statements)

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“…As demonstrated in Kiefer, Vogelsang, and Bunzel (2000), one can continue to base asymptotically valid tests ont andF even whenΩ T is not consistent. In fact,t andF will have asymptotic distributions free of nuisance parameters as long as (T 1/2 (β − β),Ω T ) has an asymptotic distribution (Ω 1/2 W (1), Ω a ) such that Ω a is independent of W (1) and with probability one Ω −1/2 Ω a Ω −1/2 is a matrix of rank greater or equal to d whose distribution does not depend on Ω or β.…”

Section: The Lack Of Robustness Of Consistent Long-run Variance Estimmentioning

confidence: 99%

“…The LRV estimator of Kiefer, Vogelsang, and Bunzel (2000), for instance, by being a continuous mapping from B T (·) to the m × m matrices in the sup norm, does not share the fragility with respect to infinitesimally small deviations of B T (·) from B(·). In contrast to the literature cited, Theorem 1 does not state that a certain set of assumptions is too weak to enable useful inference; rather it shows that a certain way of conducting inference leads to potentially arbitrary results.…”

Section: The Lack Of Robustness Of Consistent Long-run Variance Estimmentioning

confidence: 99%

“…An interesting but analytically difficult way to approach this question is to derive second-order properties of the error in rejection probability and discriminate LRV estimators on these grounds. Jansson (2004) finds that in a Gaussian location model, a certain class of inconsistent LRV estimators that contains the suggestion by Kiefer, Vogelsang, and Bunzel (2000) lead to tests with an order of magnitude smaller error in rejection probabilities than those from certain consistent LRV estimators. It might be possible to extend these results to other models and classes of LRV estimators; it suffers from the drawback, though, that it classifies LRV estimators as either nonrobust (when the error in rejection probability is of the usual order of magnitude) or robust (when the order of magnitude is smaller).…”

Section: Introductionmentioning

confidence: 99%

“…While theoretically appealing and simple to apply, inference based on consistent LRV estimators often leads to tests with bad size control in small samples with realistic amounts of dependence. As demonstrated in the seminal paper of Kiefer, Vogelsang, and Bunzel (2000) and further developed in Kiefer and Vogelsang (2002b) and Kiefer and Vogelsang (2003), the small sample approximation can be improved upon for various data generating processes when tests are based instead on certain inconsistent LRV estimators.…”

Section: Introductionmentioning

confidence: 99%

“…It is quite straightfor-1 ward to analytically describe the loss in power of tests based on inconsistent LRV estimators in the standard asymptotic thought experiment, see Kiefer, Vogelsang, and Bunzel (2000) and Kiefer and Vogelsang (2002b). It is much harder, however, to analytically describe the gain in robustness of such tests, since under standard asymptotics, also consistent LRV estimators lead to correctly sized tests.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A theory of robust long-run variance estimation

Müller

2007

Journal of Econometrics

106

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The paper studies the robustness of long-run variance estimators employed for conducting Wald-type tests in standard time series models. It is shown that all long-run variance estimators that are consistent for the variance of Gaussian White Noise lack robustness in the sense that they yield arbitrary results for some underlying process that satisfies a Functional Central Limit Theorem. An analytical measure of robustness of long-run variance estimators is suggested that captures the degree of this fragility.A family of inconsistent long-run variance estimators is derived that optimally trade off this measure of robustness against efficiency. A minor modification of these optimal estimators lead to asymptotically F-distributed test statistics under the null hypothesis, so that robust large sample inference can be conducted very similarly to well-understood small sample Gaussian inference.JEL Classification: C13, C12, C32

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Section: The Lack Of Robustness Of Consistent Long-run Variance Estimmentioning

confidence: 99%

Section: The Lack Of Robustness Of Consistent Long-run Variance Estimmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A theory of robust long-run variance estimation

Müller

2007

Journal of Econometrics

106

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HAC robust trend comparisons among climate series with possible level shifts

McKitrick

Vogelsang

2014

Environmetrics

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Comparisons of trends across climatic data sets are complicated by the presence of serial correlation and possible step-changes in the mean. We build on heteroskedasticity and autocorrelation robust methods, specifically the Vogelsang-Franses (VF) nonparametric testing approach, to allow for a step-change in the mean (level shift) at a known or unknown date. The VF method provides a powerful multivariate trend estimator robust to unknown serial correlation up to but not including unit roots. We show that the critical values change when the level shift occurs at a known or unknown date. We derive an asymptotic approximation that can be used to simulate critical values, and we outline a simple bootstrap procedure that generates valid critical values and p-values. Our application builds on the literature comparing simulated and observed trends in the tropical lower troposphere and mid-troposphere since 1958. The method identifies a shift in observations around 1977, coinciding with the Pacific Climate Shift. Allowing for a level shift causes apparently significant observed trends to become statistically insignificant. Model overestimation of warming is significant whether or not we account for a level shift, although null rejections are much stronger when the level shift is included.

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Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters

Demetrescu

Hanck

Kruse

2022

J of Applied Econometrics

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Summary 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‐ b$$ b $$” 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‐ b$$ b $$ 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.”

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Simple Robust Testing of Regression Hypotheses

Cited by 230 publications

References 10 publications

A theory of robust long-run variance estimation

A theory of robust long-run variance estimation

HAC robust trend comparisons among climate series with possible level shifts

Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters

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