Monotonic Power Research Articles

Prewhitened long-run variance estimation robust to nonstationarity

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.

Identifying changes in the distribution of income from higher‐order moments with an application to Australia

SummaryChanges in the distribution of income over time are identified based on an adjusted two‐sample version of the Neyman smooth test by using subsampling methods to approximate the sampling distribution of the test statistic when samples are not independent of each other. A range of Monte Carlo experiments show that the approach corrects for size distortions arising from dependent samples as well as generating monotonic power functions. Applying the approach to studying the distribution of income in Australia over the business cycle and the Global Financial Crisis, the empirical results highlight the importance of higher‐order moments and demonstrate that business cycles are not all alike as the relative strengths of higher‐order moments vary over phases of the cycle.

Effect of Shear History on Solid-Liquid Transition of Particulate Gel Fuels.

Investigating the structural evolution of particulate gels is a very challenging task due to their vulnerability and true flow characteristics. In this work, deeper insight into the rheological properties of gel fuels filled with fumed silica (FS) and aluminum microparticles (Al MPs) was gained by changing shear procedures. Firstly, the flow curves were found to no longer follow the monotonic power law and exhibited subtle thixotropic responses. As the shear rate increased, the gel structure underwent a transition from local shear to bulk shear in the nonlinear region after yielding. This finding reveals the prevalence of nonideal local shear in industry. Secondly, the time-dependent rheological responses demonstrated that the strength spectrum of gel fuels depends on the applied shear rate, with stress relaxation more easily observed at lower shear rates. Those results involved the structural disruption, recovery, and equilibrium of particulate gels from two scales of shear rate and shear time.

Multiple Improvements of Multiple Imputation Likelihood Ratio Tests

Multiple imputation (MI) inference handles missing data by imputing the missing values $m$ times, and then combining the results from the $m$ complete-data analyses. However, the existing method for combining likelihood ratio tests (LRTs) has multiple defects: (i) the combined test statistic can be negative, but its null distribution is approximated by an $F$-distribution; (ii) it is not invariant to re-parametrization; (iii) it fails to ensure monotonic power owing to its use of an inconsistent estimator of the fraction of missing information (FMI) under the alternative hypothesis; and (iv) it requires nontrivial access to the LRT statistic as a function of parameters instead of data sets. We show, using both theoretical derivations and empirical investigations, that essentially all of these problems can be straightforwardly addressed if we are willing to perform an additional LRT by stacking the $m$ completed data sets as one big completed data set. This enables users to implement the MI LRT without modifying the complete-data procedure. A particularly intriguing finding is that the FMI can be estimated consistently by an LRT statistic for testing whether the $m$ completed data sets can be regarded effectively as samples coming from a common model. Practical guidelines are provided based on an extensive comparison of existing MI tests. Issues related to nuisance parameters are also discussed.

A simple solution to the inadequacy of asymptotic likelihood-based inference for response-adaptive clinical trials

The present paper discusses drawbacks and limitations of likelihood-based inference in sequential clinical trials for treatment comparisons managed via Response-Adaptive Randomization. Taking into account the most common statistical models for the primary outcome—namely binary, Poisson, exponential and normal data—we derive the conditions under which (i) the classical confidence intervals degenerate and (ii) the Wald test becomes inconsistent and strongly affected by the nuisance parameters, also displaying a non monotonic power. To overcome these drawbacks, we provide a very simple solution that could preserve the fundamental properties of likelihood-based inference. Several illustrative examples and simulation studies are presented in order to confirm the relevance of our results and provide some practical recommendations.

Testing for Changes in Forecasting Performance

We consider the issue of forecast failure (or breakdown) and propose methods to assess retrospectively whether a given forecasting model provides forecasts which show evidence of changes with respect to some loss function. We adapt the classical structural change tests to the forecast failure context. First, we recommend that all tests should be carried with a fixed scheme to have best power. This ensures a maximum difference between the fitted in and out-of-sample means of the losses and avoids contamination issues under the rolling and recursive schemes. With a fixed scheme, Giacomini and Rossi’s (GR) test is simply a Wald test for a one-time change in the mean of the total (the in-sample plus out-of-sample) losses at a known break date, say m, the value that separates the in and out-of-sample periods. To alleviate this problem, we consider a variety of tests: maximizing the GR test over values of m within a prespecified range; a Double sup-Wald (DSW) test which for each m performs a sup-Wald test for a change in the mean of the out-of-sample losses and takes the maximum of such tests over some range; we also propose to work directly with the total loss series to define the Total Loss sup-Wald and Total Loss UDmax (TLUD) tests. Using theoretical analyses and simulations, we show that with forecasting models potentially involving lagged dependent variables, the only tests having a monotonic power function for all data-generating processes considered are the DSW and TLUD tests, constructed with a fixed forecasting window scheme. Some explanations are provided and empirical applications illustrate the relevance of our findings in practice. Supplementary materials for this article are available online.

Testing for shifts in mean with monotonic power against multiple structural changes

ABSTRACTIt is known that several widely used structural change tests have non-monotonic power because the long-run variance is poorly estimated under the alternative hypothesis. In this paper, we propose a modified long-run variance estimator to alleviate this problem. We theoretically show that the tests with our long-run variance estimator are consistent against large multiple structural changes. Simulation results show that the proposed test performs well in finite samples.

A Powerful Test for Changing Trends in Time Series Models

We propose a non‐parametric test for trend specification with improved properties. Many existing tests in the literature exhibit non‐monotonic power. To deal with this problem, Juhl and Xiao proposed a non‐parametric test with good power by detrending the data non‐parametrically. However, their test is developed for smooth changing trends and is constructed under the assumption of correct specification in the dynamics. In addition, their test suffers from size distortion in finite samples and imposes restrictive assumptions on the variance structure. The current article tries to address these issues. First, the proposed test allows for both abrupt breaks and smooth structural changes in deterministic trends. Second, the test employs a sieve approach to avoid the misspecification problem. Third, the extended test can be applied to the data with conditional heteroskedasticity and time‐varying variance. Fourth, the power properties under alternatives are also investigated. Finally, a partial plug‐in method is proposed to alleviate size distortion. Monte Carlo simulations show that the new test not only has good size but also has monotonic power in finite samples.

On the externality-free Shapley–Shubik index

We address the problem of extending the Shapley–Shubik index to the class of simple games with externalities introduced in Alonso-Meijide et al. (2017). On the one hand, we provide bounds for any efficient, symmetric, and monotonic power index. On the other hand, we characterize the restriction of the externality-free value of de Clippel and Serrano (2008) to the class of games under study by adapting well-known properties.

Improved Tests for Forecast Comparisons in the Presence of Instabilities

Of interest is comparing the out‐of‐sample forecasting performance of two competing models in the presence of possible instabilities. To that effect, we suggest using simple structural change tests, sup‐Wald and UDmax for changes in the mean of the loss differences. It is shown that Giacomini and Rossi () tests have undesirable power properties, power that can be low and non‐increasing as the alternative becomes further from the null hypothesis. On the contrary, our statistics are shown to have higher monotonic power, especially the UDmax version. We use their empirical examples to show the practical relevance of the issues raised.

A test for changing trends with monotonic power

We propose a powerful test for changing trends in which no nuisance parameters are needed to be nonparametrically estimated, and the only inputs required are the regression residuals under the null hypothesis. The new test allows for serial dependence, conditional heteroskedasticity and time-varying unconditional variance in error terms. Monte Carlo experiments show the test has monotonic power against abrupt or smooth structural changes in trends.

A note on monotonic power indices, smaller coalitions, and new members

Brams’ paradox of new members and Shenoy’s paradox of smaller coalitions are, in a sense, equivalent. They are both implied by the monotonicity of a power index: while the first is exhibited on every simple game that is not strong, the latter can be observed on every simple game in which players are not almost symmetric. For the Shapley–Shubik index, this symmetry condition is not only necessary but also sufficient to avoid the paradox of smaller coalitions.

Testing for structural change under non‐stationary variances

Non‐stationarity of the volatility process reflects low‐frequency volatility changes of an economic time series, and its theoretical and empirical relevance has been widely recognized. We investigate how it affects cumulative sum (CUSUM) related tests for structural change in regression coefficients. Non‐stationary variances generally invalidate standard structural change tests by introducing an infinite‐dimensional nuisance parameter in the limit distribution, and we propose robust alternatives. We also show that the practical relevance of the non‐monotonic power issue, which is peculiarly associated with the test for changing mean, is mitigated (although the power against a small change is reduced) if there is comparable change in volatility levels. The results are useful to validate/modify a test to ensure monotonic power. Simulations and an empirical example provide finite‐sample evidence of the theoretical findings.

Restoring monotonic power in Wald/LM-type tests

Wald/LM-type tests for a shift in mean often exhibit nonmonotonic power, due to incorrect estimation of long-run variance. In this paper, we propose a robust estimator of long-run variance that is built on nonparametric regression residuals and always converges to the true long-run variance under both the null and the alternative hypothesis. Monte Carlo experiments show that the modified tests have monotonic power against the mean with single or multiple breaks in finite samples.

Coalition formation in general apex games under monotonic power indices

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.

Power monotonicity in detecting volatility levels change

We show that the CUSUM and LM tests for structural change in the volatility process enjoy monotonic power. The framework is general including many recently proposed non-stationary GARCH-type models. The result is in contrast to the well-known issue of non-monotonic power for the CUSUM-based tests for changing mean. Simulations and an empirical example provide further support.

Piecewise Polynomial Expression of Beach Profiles

This paper advances a piecewise polynomial-based concept of beach profile geometric representation, the Piecewise Weighted Polynomial Interpolation Function (PWPIF) expression. Conventional monotonic power function or exponential function expressions of beach profile do not correlate well with actual field conditions. An alternative approach, the cubic spline interpolation function, has problems with overfluctuation. The PWPIF expression is both a conceptual and practical beach profile geometric model with a higher degree of approximation to reality in that (i) it correctly expresses the undulated morphology (e.g., bar-trough); (ii) it copes well with the overfluctuation that the cubic spline interpolation curve sustains; (iii) it gives a more realistic representation of beach profiles without missing important morphological information contained in seemingly irregular variation appearances, as it makes full use of all the gathered topographical information in establishing its coefficients; and (iv) it represents a flexible and all-inclusive approach towards expressing multiple beach profile types. The PWPIF expression has been tested against 667 sets of beach profile data measured from actual field as well as laboratory conditions. As a spatial model, it can act as a more-realistic geometric framework in beach analysis, helping to characterise beach morphological elements (beach position, slope, and volume). Temporal analysis of profile changes also benefits from this geometric model.

Tests for a mean shift with good size and monotonic power

This paper proposes tests for a mean shift based on a new hybrid estimator of the long-run variance. It is shown that these tests can bypass the non-monotonic power problem of the LM tests while maintaining adequate size properties.

Tests for changing mean with monotonic power

Abstract Several widely used tests for a changing mean exhibit nonmonotonic power in finite samples, due to “incorrect” estimation of nuisance parameters under the alternative. In this paper, we study the issue of nonmonotonic power in testing for changing mean. We investigate the asymptotic power properties of the tests, using a new framework where alternatives are characterized as having “large” changes. The asymptotic analysis provides a theoretical explanation to the power problem. Modified tests that have monotonic power against a wide range of alternatives of structural change are proposed. Instead of estimating the nuisance parameters based on ordinary least squares residuals, the proposed tests use modified estimators, based on nonparametric regression residuals. It is shown that tests based on the modified long-run variance estimator provide an improved rate of divergence of the tests under the alternative of a change in mean. Tests for structural breaks based on such an estimator are able to remain consistent, while still retaining the same asymptotic distribution under the null hypothesis of constant mean.

Limits on the changes in the gravitational constant from nucleosynthesis

Due to the recent all-sky, high-precision measurement of microwave background anisotropies by WMAP, a value for baryon-to-photon ratio η was obtained. At the WMAP value for η, the 4HE abundance was predicted. In this article we use a simple semi-analytical method with 4He predicted and measured values to place a limit on the variation of the gravitational constant G. We find using a conservative range for the measured values for Yp, that ΔG/G is constrained between −0.26 and 0.15. If we assume a monotonic power law time dependence G∼t−β then β values is constrained between −0.008 and 0.0038, which translate into \(-2.8\times 10^{-13}~\mbox{yr}^{-1}<\dot{G}/G<6.0\times 10^{-13}~\mbox{yr}^{-1}\) . This compares well with results obtained by others using full numerical analysis.