Moment Conditions Research Articles

Efficient and Robust Estimation of the Generalized LATE Model

This article studies the estimation of causal parameters in the generalized local average treatment effect (GLATE) model, which expands upon the traditional LATE model to include multivalued treatments. We derive the efficient influence function (EIF) and the semiparametric efficiency bound (SPEB) for two types of causal parameters: the local average structural function (LASF) and the local average structural function for the treated (LASFT). The moment conditions generated by the EIF satisfy two robustness properties: double robustness and Neyman orthogonality. Based on the robust moment conditions, we propose the double/debiased machine learning (DML) estimator for estimating the LASF. The DML estimator is well-suited for high dimensional settings. We also propose null-restricted inference methods that are robust against weak identification issues. As an empirical application of these methods, we examine the potential health outcome across different types of health insurance plans using data from the Oregon Health Insurance Experiment.

Staying positive: challenges and solutions in using pure multiplicative ETS models

Abstract Accepted by: Zied Babai Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue, we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works.

Uniform asymptotics for finite-time ruin probabilities of a bidimensional compound risk model with stochastic returns

Consider a continuous-time bidimensional compound risk model with stochastic returns, where an insurance company operates two lines of business at the same time and is allowed to invest its wealth into financial assets. In this model, each accident may cause a random number of heavy-tailed claims and the claim sizes from the same line of business are upper tail asymptotically independent, while the accident arrival processes from different lines of business are arbitrarily dependent. Under some moment conditions on the accident arrival processes, some uniform asymptotic formulae for finite-time ruin probabilities are established.

Research on the Relationship between Dynamic Characteristics and Friction Torque Fluctuation of CMGB under the Condition of Time-Varying Moment

In this paper, a dynamic simulation analysis model was established for CMGB (control moment gyroscope bearing) under the conditions of time-varying moment. The influences of the moment’s response time, axial preload, and working temperature on the dynamic characteristics and friction torque of CMGB were analyzed, and the relevant verification tests were conducted. The results show that the friction torque fluctuation of CMGB directly corresponds to the dynamic characteristics. The faster the response time of the time-varying moment, the larger the friction torque fluctuation of CMGB. The larger preload minimizes the difference in the ball’s loading state, which is the actual reason for reducing the friction torque fluctuation. Moreover, as the working temperature increases, the friction torque fluctuation of CMGB decreases.

Exact convergence rate in central limit theorem for a supercritical branching process with immigration in a random environment

Let {Z n } be a supercritical branching process with immigration in an independent, identically distributed(i.i.d.) environment ξ. The Berry-Esseen bound for log⁡Z n has been established by Wang et al. (2021). To refine that, under the less restrictive moment conditions, we calculate the exact convergence rate in the central limit theorem for log⁡Z n under the annealed law.

Machine learning tabulation of thermochemistry for turbulent dimethyl ether (DME) flames

The present work applies a machine learning tabulation methodology for the thermochemistry of dimethyl ether (DME), a typical biodiesel fuel, to accelerate the real-time computation of a large-size DME mechanism in turbulent non-premixed combustion. This approach is known as the hybrid flamelet/random data and multiple multilayer perceptrons (HFRD-MMLP) method (Ding et al., 2021). The essence of the HFRD-MMLP method lies in the generation of training data using the HFRD approach, which enhances the capacity of generalisation for the reactive composition space encountered in practical turbulent combustion by using the random process to expand the training dataset from laminar flamelets. The MMLP artificial neural networks (ANNs) are then trained to predict different composition states, aiming to improve the accuracy of ANN predictions. To validate the effectiveness of the ANNs, they are initially tested on 1-D laminar flame simulations with varying strain rates. Subsequently, a test is conducted on Sandia non-premixed turbulent DME series flames D and F, with an increasing jet Reynolds Number. The results regarding species mole fractions and temperature show overall excellent agreement with the direct integration method. The HFRD-MMLP method achieves speed-up factors of over 16 and 10 for the reaction step, and total computational costs, respectively, in the LES-PDF simulation with the DME mechanism in this work, surpassing the speed-up factors of approximately 12–14, and below 5 for the reaction step, and total time costs, respectively, in previous works on GRI-1.2 mechanism for CH4 (Ding et al., 2021) and CH4/H2 (Ding et al., 2022) combustion. This indicates that the HRFD-MMLP method is highly effective for mechanisms of large size in reducing the computational cost by avoiding a significant number of highly stiff ordinary differential equations (ODEs) integration. This approach can be applied in real-time calculations of reaction source terms in methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and laminar flame computation.

Tighter Bounds on Transient Moments of Stochastic Chemical Systems

The use of approximate solution techniques for the Chemical Master Equation is a common practice for the analysis of stochastic chemical systems. Despite their widespread use, however, many such techniques rely on unverifiable assumptions and only a few provide mechanisms to control the approximation error quantitatively. Addressing this gap, Dowdy and Barton (J Chem Phys 149(7):074103, 2018) proposed an optimization-based technique for the computation of guaranteed bounds on the moment trajectories associated with stochastic chemical systems, thereby providing a general framework for rigorous uncertainty quantification. Here, we present an extension of this method. The key contribution is a new hierarchy of convex necessary moment conditions that build upon partitioning of the time domain. These conditions reflect the temporal causality that is inherent to the moment trajectories associated with stochastic processes described by the Chemical Master Equation and can be strengthened by simple refinement of the time domain partition. Analogous to the original method, these conditions generate a hierarchy of semidefinite programs that furnishes monotonically improving bounds on the trajectories of the moments and related statistics of stochastic chemical systems. Compared to its predecessor, the presented hierarchy produces bounds that are at least as tight and features new bound tightening mechanisms such as refinement of the time domain partition which often enable the computation of dramatically tighter bounds with lower computational cost. We analyze the properties of the presented hierarchy, discuss some aspects of its practical implementation and demonstrate its merits with several examples.

Inference in models with partially identified control functions

In multiple contributions to the literature, James L. Powell and coauthors have developed estimators for semiparametric models where sample selectivity and/or endogeneity can be handled through a “control function”. Their methods rely on pairwise comparisons of observations which match (asymptotically) the control functions. Conditional on this matching, a moment condition can identify the parameters of the model. However, there exist instances where the control functions are unobserved, but we have bounds for them which depend on observable covariates. These bounds can arise directly from the nature of the data available (e.g, with interval data), or they can be derived from an economic model. The inability to observe the control functions precludes the matching proposed in Powell’s methods. In this paper we show that, under certain conditions, testable implications can still be obtained through pairwise comparisons of observations for which the control-function bounds are disjoint. Testable implications now take the form of pairwise functional inequalities. We propose an inferential procedure based on these pairwise inequalities and we analyze its properties.

General spatial model meets adaptive shrinkage generalized moment estimation: Simultaneous model and moment selection

Spatial data are widely used in various scenarios of life and are highly valued, and their analysis and research have achieved remarkable results. Spatial data have spatial effects and do not satisfy the assumption of independence; thus, the traditional econometric analysis methods cannot be directly used in spatial models, and the spatial autocorrelation and spatial heterogeneity of spatial data make the research more complicated and difficult. Generalized moment estimation(GMM) is a powerful tool for statistical modeling and inference of spatial data. Considering the case where there is a set of correctly specified moment conditions and another set of possibly misspecified moment conditions for spatial data, this paper proposes a GMM shrinkage method to estimate the unknown parameters for spatial autoregressive model with spatial autoregressive disturbances. The proposed GMM estimators are shown to enjoy oracle properties; i.e., it selects the valid moment conditions consistently from the candidate set and includes them into estimation automatically. The resulting estimator is asymptotically as efficient as the GMM estimator based on all valid moment conditions. Monte Carlo studies show that the method works well in terms of valid moment selection and the finite sample properties of its estimators.

Detecting identification failure in moment condition models

This paper develops an approach to detect identification failure in moment condition models. This is achieved by introducing a quasi-Jacobian matrix computed as the slope of a linear approximation of the moments on an estimate of the identified set. It is asymptotically singular when local and/or global identification fails, and equivalent to the usual Jacobian matrix which has full rank when the model is globally and locally identified. Building on this property, a simple test with chi-squared critical values is introduced to conduct subvector inferences allowing for strong, semi-strong, and weak identification without a priori knowledge about the underlying identification structure. Monte-Carlo simulations and an empirical application to the Long-Run Risks model illustrate the results.

LINEAR GROWTH OF TRANSLATION LENGTHS OF RANDOM ISOMETRIES ON GROMOV HYPERBOLIC SPACES AND TEICHMÜLLER SPACES

Abstract We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation lengths. As a corollary, almost every random walk on mapping class groups eventually becomes pseudo-Anosov, and almost every random walk on $\mathrm {Out}(F_n)$ eventually becomes fully irreducible. If the underlying measure further has finite first moment, then the growth rate of translation lengths is equal to the drift, the escape rate of the random walk. We then apply our technique to investigate the random walks induced by the action of mapping class groups on Teichmüller spaces. In particular, we prove the spectral theorem under finite first moment condition, generalizing a result of Dahmani and Horbez.

Fuzzy clustering of time series based on weighted conditional higher moments

This paper proposes a new approach to fuzzy clustering of time series based on the dissimilarity among conditional higher moments. A system of weights accounts for the relevance of each conditional moment in defining the clusters. Robustness against outliers is also considered by extending the above clustering method using a suitable exponential transformation of the distance measure defined on the conditional higher moments. To show the usefulness of the proposed approach, we provide a study with simulated data and an empirical application to the time series of stocks included in the FTSEMIB 30 Index.

“Good” and “bad” volatilities: a realized semivariance GARCH approach

ABSTRACT In this article, we explore the realized semivariation measures using high-frequency intraday data within the framework of realized semivariance GARCH by taking an in-depth look. We derive general theoretical expressions for moment conditions of returns and realized semivariation measures, providing a convenient approach to investigate the statistical properties of realized semivariation dynamics. Notably, the introduction of threshold effects in the model reveals several intriguing empirical findings. One significant discovery is that during a substantial decline in returns, the negative realized semivariance exerts a more influential impact on future volatility compared to its positive counterpart. We further examine the forecasting performance under a realized semivariance heterogeneous autoregression environment. The results demonstrate that the inclusion of thresholds and the adoption of an optimal threshold level generally enhance the accuracy of volatility forecasting.

Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification are important because they are relatively easy to simulate. One does not have to care about the distribution of their jumps which is always difficult to find. Among those processes with the continuous path are the Ornstein–Uhlenbeck process, the Gamma process, the process with Arcsin or Wigner margins and the Theta functions as the transition densities and others. We give a simple criterion for the stationary process to have a continuous path modification expressed in terms of skewness and excess kurtosis of the marginal distribution.

Local linearization based subvector inference in moment inequality models

This paper introduces a bootstrap-based profiling inference method for subvectors in moment inequality models following insights from Bugni et al. (2017). Compared to their paper, the new method calculates the critical value by searching over a local neighborhood of a pre-estimator, instead of the whole null parameter space, to profile out nuisance parameters. In this way, non-linear moment conditions are simplified by linear expansion and the bootstrap iterates over quadratic programming problems, which significantly simplifies and accelerates computation. This method controls asymptotic size uniformly over a large class of data generating processes. In the Monte Carlo simulations, the new procedure improves upon the computing time of Bugni et al. (2017) and Kaido et al. (2019) significantly. I provide an empirical illustration estimating an airline entry game.

Risk characteristics and connectedness in cryptocurrency markets: New evidence from a non-linear framework

Existing research pays less attention to the risk characteristics and connectedness of higher moments of cryptocurrencies. We dynamically analyze the risk characteristics of cryptocurrencies and their connectedness at four levels: return, volatility, skewness, and kurtosis. First, there are price bubbles in five popular cryptocurrencies, with long bubble periods during the COVID-19 epidemic. The volatility, skewness and kurtosis of cryptocurrencies are characterized by high persistence, with the exception of BNB. Second, the connectedness between the five cryptocurrencies is significant at higher moment conditions. The results for time-varying connectedness show that the total spillover of volatility, skewness and kurtosis varies over a wider range than returns, and that the total spillover of returns, volatility and skewness peaks during COVID-19. According to the pairwise results, there is strong connectedness between Ether and Bitcoin at the level of returns, volatility, skewness, and kurtosis, which is more significant at higher moments. Third, the role of cryptocurrencies changes not only over time, but also over order moments. The cryptocurrency market experienced significant volatility during 2018 and the first half of 2019, with Bitcoin being the most significant net exporter of returns and volatility spillovers. Cardano is a net exporter of both skewness and kurtosis spillover, and it is highly persistent with respect to volatility, skewness, and kurtosis. Overall, the leader in risk spillover at all order moments is Ether, and the net receiver is BNB.

Generalized Dinesh–Umesh–Sanjay generalized exponential distribution with application to engineering data

Several academics have expanded the generalized exponential distribution. The generalized Dinesh–Umesh–Sanjay generalized exponential (GDUS-GE) distribution with three parameters is introduced. The GDUS-GE distribution outperforms the moment exponential distribution in terms of fit. For numerous GDUS-GE distribution characteristics, exact formulations for ordinary moments, incomplete and conditional moments, the moment generating function, and information measures are discovered. The maximum likelihood approach was used to estimate model parameters. A simulated study was used to explore the estimators’ behavior. Two real-world datasets were used to assess the practical significance of the GDUS-GE distribution. In terms of performance, we demonstrate that the GDUS-GE distribution outperforms all other competing models.

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

$U$-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. $U$-statistics generalise the empirical mean of a random variable $X$ to sums over every $m$-tuple of distinct observations of $X$. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional $U$-statistics. In the present work, we provide a new class of estimators of conditional $U$-statistics. More precisely, we investigate the conditional $U$-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over $\varphi \in \mathscr{F}$ for a suitably restricted class $\mathscr{F}$, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional $U$-statistics processes. We discuss the wild bootstrap of the conditional $U$-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.

Unveiling the diversification capabilities of carbon markets in NFT portfolios

This empirical study investigates the potential of carbon markets in reducing the downside risk of NFT portfolios. Employing a monthly rebalance experiment and considering higher order conditional moments, we dynamically measure the tail risk of NFT portfolios over an out-of-sample period. Our results show that introducing CO2 emission allowance (EUA) futures in NFT portfolios allows for a systematic mitigation of risk via reduction of volatility and kurtosis and steepening of skewness. Empirical evidence also reveals the outperformance of NFT portfolios that include EUA futures.

Random walks on mapping class groups

This survey is concerned with random walks on mapping class groups. We illustrate how the actions of mapping class groups on Teichmüller spaces or curve complexes reveal the nature of random walks and vice versa. Our emphasis is on the analogues of classical theorems such as laws of large numbers and central limit theorems and the properties of harmonic measures under optimal moment conditions. We also explain the geometric analogy between Gromov hyperbolic spaces and Teichmüller spaces that has been used to copy the properties of random walks from one to the other.