Adaptive market hypothesis: The story of the stock markets and COVID-19 pandemic

Since the level of markets’ information efficiency is key to profiteering by strategic players, Shocks; such as the COVID-19 pandemic, can play a role in the nature of markets’ information efficiency. The martingale difference and conditional heteroscedasticity tests are used to evaluate the Adaptive form of market efficiency for four (4) major stock market indexes in the top four affected economies during the COVID-19 pandemic (USA, Brazil, India, and Russia). Generally, based on the martingale difference spectral test, there is no evidence of a substantial change in the levels of market efficiency for the US and Brazilian stock markets in the short, medium, and long term. However, in the long term, the Indian stock markets became more information inefficient after the coronavirus outbreak while the Russian stock markets become more information efficient. Intuitively, these affect the forecastability and predictability of these markets’ prices and/or returns. Thereby, informing the strategic and trading actions of stock investors (including arbitrageurs) towards profit optimization, portfolio asset selection, portfolio asset adjustment, etc. Similar policy implications are further discussed.     

Bayesian modeling of joint and conditional distributions

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.     

Testing for multivariate volatility functions using minimum volume sets and inverse regression

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) in a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the so-called ‘smiling effect’, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.     

基于分组的异方差检验和两阶段估计

本文提出了一种基于分组的异方差检验法，并给出了存在异方差时的两阶段估计。     

Inference on endogenously censored regression models using conditional moment inequalities

Under a quantile restriction, randomly censored regression models can be written in terms of conditional moment inequalities. We study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring, endogenous censoring and endogenous regressors. These inequalities restrict the parameters to a set. We show regular point identification can be achieved under a set of interpretable sufficient conditions. We then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content. Our method obviates the need for nonparametric estimation, which would require the selection of smoothing parameters and trimming procedures. Without the point identification conditions, our objective function can be used to do inference on the partially identified parameter. Maintaining the point identification conditions, we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest, and has an asymptotically normal distribution. A small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance.     

Estimation of technical inefficiency effects using panel data and doubly heteroscedastic stochastic production frontiers

In previous studies, measures of technical inefficiency effects derived from stochastic production frontiers have been estimated from residuals which are sensitive to specification errors. This study corrects for this inaccuracy by extending the doubly heteroscedastic stochastic cost frontier suggested by Hadri (1999) to the model for technical inefficiency effects. This model is a stochastic frontier production function for panel data as proposed by Battese and Coelli (1995). The study uses, for illustration of the techniques, data on 101 mainly cereal farms in England. We find that the correction for heteroscedasticity is supported by the data. Both point estimates and confidence intervals for technical efficiencies are provided. The confidence intervals are constructed by extending the “Battese-Coelli” method reported by Horrace and Schmidt (1996) by allowing the technical inefficiency to be time varying and the disturbance terms to be heteroscedastic. The confidence intervals reveal the precision of technical efficiency estimates and show the deficiencies of making inferences based exclusively on point estimates. First version received: March 2000/Final version received: Oct. 2001 RID="*" ID="*"  The authors are grateful to the Economic and Social Research Council for access to their Data Archive which has provided the data for this research. We are indebted to Badi Baltagi and two anonymous referees for their helpful comments and suggestions. The usual caveat applies.     

A test of Hotelling’s Valuation Principle for nonrenewable resources

A recent study by Cairns and Davis (1998) tested and rejected the Hotelling Valuation Principle (HVP) using cross-sectional data on gold mines. But a replication of that study using the same data suggests the presence of heteroscedastic errors. In contrast to the results of ordinary least squares regressions, robust estimation and weighted least squares results indicate that the HVP may not be rejected at conventional levels of significance. Moreover, the alternative valuation equations proposed by Cairns and Davis can require additional and often unavailable information regarding mineral production. Matched pairs tests indicate that prediction accuracy is roughly comparable across all of the equations examined.Revisions to this paper were completed during a sabbatical at the Life Cycle Institute in the Catholic University of America. I thank Ernest M. Zampelli, Philip Pfaff, two anonymous referees, and the editors for helpful comments. Any errors are my own.First version received: May 2003/Final version received: April 2004     

Monitoring processes with changing variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension has required the consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process.     

Two-stage rank estimation of quantile index models

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246–269; Annals of Statistics 19 (1991b) 760–777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model.     

Modelling Exogenous Variables in Human Capital Formation through a Heteroscedastic Stochastic Frontier

The objective of this paper is to suggest the use of a stochastic frontier model in which the inefficiency component is heteroscedastic in the measurement of technical efficiency in Human Capital Formation in the Italian University System. The heteroscedastic frontier model enables one to consider the effect of students’ individual characteristics and the influences of the resources and organization of the specific faculty on efficiency. The suggested model is applied to the case of Florence University graduates. The results show that the model specification is strongly supported by the data. Moreover, the suggested specification explains variation in technical efficiency in terms of graduate-specific factors. The technical efficiency scores obtained are comparable across faculties.