Use Of Higher Moments Research Articles

The relative importance of economic policy uncertainty and geopolitical risk on U.S. REITs returns

PurposeOur aim in this study is to investigate the relative importance of the economic policy uncertainty and of the geopolitical risk on U.S. REITs (Real Estate Investment Trusts) returns with a special focus on the different real estate sectors.Design/methodology/approachWe use an augmented Fama-French (1993)’s asset pricing model, including economic policy uncertainty indices (EPU), introduced by Baker et al. (2016), and geopolitical risk indices (GPR) recently developed by Caldara and Iacoviello (2022), to price the potential risk factors for U.S. Nareit indices returns. To obtain robust economic results, we correct for the problems of errors-in-variables in linear asset pricing models; we advocate the use of higher moments estimators as instruments in a generalized method of moments (GMM) framework.FindingsOur results report that economic policy uncertainty (EPU), and geopolitical risk (GPR) are priced for the different Nareit sectors for the last three decades. The GPR index stands as a relevant risk factor. The coefficient estimates are low compared to Fama-French risk factors. They are higher for Shopping Centers, Retail and Region Malls and lower for Health Care and Lodging/Resorts. EPU indices are also priced and less statistically significant. Health Care sector, followed by Shopping Centers and Retail are the most policy-sensitive sectors.Practical implicationsIn their “2023–2024 Top Ten Issues Affecting Real Estate” “political unrest and global economic health” is ranked 1 issue by the Counselors of Real Estate. Our results report that economic policy uncertainty and geopolitical risk are priced for the different Nareit sectors. They suggest implications for investors, insurers, bankers, policymakers and other stakeholders. The geopolitical risk index (GPR) stands as a relevant and significant risk factor for REITs returns.Originality/valueBased on parsimonious robust asset pricing models, the results shed a new light on the relative importance of geopolitical risk and economic policy uncertainty in the real estate sector, with a special focus on the different U.S. REITs sectors. They suggest possible implications for investors, insurers, bankers, policymakers and other stakeholders in a context marked by higher uncertainty shocks and geopolitical risks.

Sensitivity Analysis and Extensions of Testing the Causal Direction of Dependence: A Rejoinder to Thoemmes (2019)

A commentary by Thoemmes on Wiedermann and Sebastian’s introductory article on Direction Dependence Analysis (DDA) is responded to in the interest of elaborating and extending direction dependence principles to evaluate causal effect directionality. Considering Thoemmes’ observation that some DDA principles are already well-established in machine learning, we argue that several other connections between DDA and research lines in theoretical statistics, econometrics, and quantitative psychology exist, suggesting that DDA is best conceptualized as a framework that summarizes and extends existing knowledge on properties of linear models under non-normality. Further, Thoemmes articulates concerns about assumptions of error distributions used in our main article and presents an artificial data example in which some DDA tests have suboptimal statistical power. We present extensions of DDA to entirely relax distributional assumptions about errors and describe two sensitivity analysis approaches to critically evaluate DDA results. Both sensitivity approaches are illustrated using Thoemmes’ artificial data example. Incorporating DDA sensitivity results yields correct causal conclusions. Thus, overall, we stay with our initial conclusion that the use of higher moments in causal inference constitutes an exciting open research area.

The dependence of cirrus gamma size distributions expressed as volumes in N0‐λ‐μ phase space and bulk cloud properties on environmental conditions: Results from the Small Ice Particles in Cirrus Experiment (SPARTICUS)

AbstractThe variability of cirrus ice microphysical properties is investigated using observations obtained during the Small Particles in Cirrus (SPARTICUS) campaign. An existing approach that represents a size distribution (SD) as a single gamma function using an ellipsoid of equally realizable solutions in (N0, λ, μ) phase space is modified to automatically identify multiple modes in SDs and characterize each mode by such an ellipsoid. The modified approach is applied to ice crystals with maximum dimension D > 15 µm collected by the 2‐D stereo and 2‐D precipitation probes on the Stratton Park Engineering Company Learjet. The dependencies of N0, μ, and λ from each mode, total number concentration, bulk extinction, ice water content (IWC), and mass median maximum dimension Dmm as a function of temperature T and cirrus type are then analyzed. The changes in the observed codependencies between N0, μ, and λ, bulk extinction, IWC, and Dmm with environmental conditions indicate that particles were larger at higher T during SPARTICUS. At most two modes were observed in any SD during SPARTICUS, with the average boundary between them at 115 µm, similar to past studies not using probes with shatter mitigating tips and artifact removal algorithms. The bimodality of the SDs increased with T. This and the differences in N0, μ, and λ between the modes suggest that particles with smaller D nucleated more recently than particles with larger D, which grew via vapor deposition and aggregation. Because smaller crystals, whose concentrations are uncertain, make marginal contributions to higher order moments, the use of higher moments for evaluating model fields is suggested.

Determination of absorption changes from moments of distributions of times of flight of photons: optimization of measurement conditions for a two-layered tissue model

Time-resolved near-infrared spectroscopy allows for depth-selective determination of absorption changes in the adult human head that facilitates separation between cerebral and extra-cerebral responses to brain activation. The aim of the present work is to analyze which combinations of moments of measured distributions of times of flight (DTOF) of photons and source-detector separations are optimal for the reconstruction of absorption changes in a two-layered tissue model corresponding to extra- and intra-cerebral compartments. To this end we calculated the standard deviations of the derived absorption changes in both layers by considering photon noise and a linear relation between the absorption changes and the DTOF moments. The results show that the standard deviation of the absorption change in the deeper (superficial) layer increases (decreases) with the thickness of the superficial layer. It is confirmed that for the deeper layer the use of higher moments, in particular the variance of the DTOF, leads to an improvement. For example, when measurements at four different source-detector separations between 8 and 35 mm are available and a realistic thickness of the upper layer of 12 mm is assumed, the inclusion of the change in mean time of flight, in addition to the change in attenuation, leads to a reduction of the standard deviation of the absorption change in the deeper tissue layer by a factor of 2.5. A reduction by another 4% can be achieved by additionally including the change in variance.

Closed‐form parameter estimates for a truncated gamma distribution

AbstractGamma distributions are used by atmospheric scientists to model the distribution of raindrop diameters. However, the recording instruments (known as disdrometers) are unable to record the sizes of the smallest drops, so that the recorded distribution (which consists of group frequencies) is truncated. Although the method of maximum likelihood can be used to estimate the parameters of such a truncated and grouped distribution, this method is not customarily used by practitioners. Their preference has been for the very simple method of moments. Many different combinations of moments have been suggested, with a preference for the use of higher moments both because of their physical relevance (to the volume of water, the attenuation of radio signals or radar reflectivity) and because of the low‐end truncation. However, the difficulty in accurately estimating higher moments leads to these estimates often being biased and invariably having high variance. Recognising the attraction of a computationally simple procedure, we introduce a method that uses a combination of moment relationships and weighted linear regression to give explicit formulae for parameter estimates. We compare the performance of these estimates with both maximum likelihood and moment estimates for untruncated, singly truncated and doubly truncated gamma distributions. We show that our simple closed‐form estimates compare favourably with the optimal maximum likelihood estimates. Copyright © 2007 John Wiley & Sons, Ltd.

Coarse scale models of two phase flow in heterogeneous reservoirs: volume averaged equations and their relationship to existing upscaling techniques

Coarse scale equations applicable to two phase flow in heterogeneous reservoirs are developed via a volume average of the fine scale saturation equation. The resulting coarse scale description, in the form of an average saturation equation and a sequence of moment equations, is then used to assess several methods for the upscaling of detailed reservoir characterizations. The approaches considered are the use of pseudo‐relative permeabilities, the nonuniform coarsening of the fine grid geostatistical model, and the use of higher moments of the fine scale variables. Using the volume averaged equations as a framework, the underlying assumptions, strengths and limitations of each of these methods are discussed. Previous findings demonstrating the accuracy of coarse scale relative permeability functions based on higher moments are readily explained in terms of the volume average saturation and moment equations. Finally, the volume averaged equations are simplified for the unit mobility ratio case and applied to the direct solution of a model coarse scale problem.

Use of Higher Moments for the Description of Upscaled, Process Independent Relative Permeabilities

Summary Traditional approaches for the scale up of highly detailed reservoir descriptions to the coarser scales more appropriate for reservoir simulation often rely on the use of pseudo relative permeabilities. Two of the major limitations in the use of pseudo relative permeabilities are the process dependency inherent in the resulting curves and the need for a different set of curves in each coarse scale grid block. In this paper, these limitations are illustrated and quantified through numerical simulations of viscous dominated displacements in fine scale, heterogeneous, two dimensional systems. It is concluded that the functional form of traditional pseudo relative permeability descriptions is too limited to capture a wide variety of flow behavior and that an ‘extended description,’ in which the upscaled relative permeabilities depend on variables in addition to the phase saturations, is required. The additional variables we propose are higher moments of the fine scale variables, specifically the variance of saturation, the variance of pressure and the velocity-saturation covariance. It is then shown that these new variables are capable of accurately correlating upscaled relative permeabilities for a variety of displacements in a process independent manner; i.e., the extended description can account for varying inlet conditions and permeability realizations. The practical use of this methodology in an actual reservoir simulation will, however, require the derivation and solution of coarse scale evolution equations for the moments.

Estimation of dispersion in estuaries by a self-consistent method

Longitudinal and transverse dispersion in estuaries may be determined in principle by measuring the change in time of the concentration field of a water soluble dye. In practice, measurements may take the form of several sampling runs crossing the dye patch. The coefficients of dispersion are usually estimated from the second moments of the concentration field; the use of second moments, in particular, introduces errors because measurements at long times or distance are unduly emphasized. A self-consistent method, free of the disadvantages inherent in the use of higher moments, is described in which the distribution of concentration in space is related to the zeroth spatial moment of concentration. In this formulation, based upon sampling runs across the dye patch, the concentration field in the estuary may be directly and simply related to the dispersion coefficients in both the intercept and gradient of a linear graph. The methods are illustrated by the characterization of a series of experiments in the Inner Estuary of Milford Haven.

The use of higher moments to extract transport data from chromatographic adsorption experiments

A chromatographic method based on analysis of the first four moments of the response peak has been developed and applied to the analysis of experimental data for the sorption of some light gases on several zeolitic adsorbents. Axial dispersion, intra-particle diffusivities and adsorption equilibrium were found using this method and were shown to be consistent with the values derived by other methods of analysis. The proposed methods provides a significant improvement over methods of analysis that use only the first and second moments because the quantity of data necessary to derive the model parameters is reduced.