On the Assessment of Homogeneity in a Uniform Regression Model

When conducting an exploratory analysis of the data and the subsequent construction of functional dependencies between the observed phenomena, it is often necessary to assess the degree of dependence between the studied data. The basis for obtaining such criteria with a probabilistic approach usually includes the correlation component of the sample. The choice of the used indicator directly depends on the methods of studying the sample, as well as the tools for constructing the model. In most cases, at the initial stage of modeling, it is precisely the homogeneity estimates of the sample that are studied, a good selection of which can reduce the complexity of constructing the relationship between the data.In this paper, we study a method for assessing the uniformity of sample data when constructing a uniform regression model. The first part of the paper describes the correlation coefficient for the L∞ regression, studies the interval of its change, describes the geometric interpretation and the algorithm for constructing this indicator. In the second part of the paper, we study the method of constructing an indicator of "concentration" of the sample. For this, formulas are derived that relate the correlation coefficient to the magnitude of the original sample. In conclusion, a description is given of the algorithms for constructing the considered indicators, and conclusions are drawn about the complexity of these algorithms.

Effects of Idiosyncratic Volatility in Asset Pricing

This paper aims to evaluate the effects of the aggregate market volatility components - average volatility and average correlation - on the pricing of portfolios sorted by idiosyncratic volatility, using Brazilian data. The study investigates whether portfolios with high and low idiosyncratic volatility - in relation to the Fama and French model (1996) - have different exposures to innovations in average market volatility, and consequently, different expectations for return. The results are in line with those found for US data, although they portray the Brazilian reality. Decomposition of volatility allows the average volatility component, without the disturbance generated by the average correlation component, to better price the effects of a worsening or an improvement in the investment environment. This result is also identical to that found for US data. Average variance should thus command a risk premium. For US data, this premium is negative. According to Chen and Petkova (2012), the main reason for this negative sign is the high level of investment in research and development recorded by companies with high idiosyncratic volatility. As in Brazil this type of investment is significantly lower than in the US, it was expected that a result with the opposite sign would be found, which is in fact what occurred.

A Waveguide-Invariant-Based Warping Operator and Its Application to Passive Source Range Estimation

A formula for the instantaneous phase of the cross-correlation function of two different modes using the relationship between the horizontal wavenumber difference and frequency described by the waveguide invariant is deduced in this paper. Based on the formula, a waveguide-invariant-based warping operator suitable for both reflected and refracted modes in shallow water at low frequency is presented, providing an effective tool to filter the cross-correlation function of modes from the signal autocorrelation function. Using the phase of the filtered cross-correlation component in the frequency domain, a passive source ranging method on a single hydrophone is proposed. Simulated and experimental data using impulsive signals verify the validity of the derived warping operator and source ranging method.