Heterogeneous Tail Generalized Common Factor Modeling

ABSTRACTThis article introduces a new asymmetric distribution constructed by assuming the multivariate normal mean-variance mixture model. Called normal mean-variance mixture of the Lindley distribution, we derive some mathematical properties of the new distribution. Also, a feasible maximum likelihood estimation procedure using the EM algorithm and the asymptotic standard errors of parameter estimates are developed. The performance of the proposed distribution is illustrated by means of real datasets and simulation analysis.

Mixtures of normal distributions provide a useful modeling extension of the normal distribution—both univariate and multivariate. Unlike the normal distribution, mixtures of normals can capture the kurtosis (fat tails) and nonzero skewness often necessary for accurately modeling a variety of real-world variables. An efficient analytical Monte Carlo method is proposed for considering multivariate mixtures of normal distributions having arbitrary covariance matrices. The method consists of a linear transformation of a multivariate normal having a computed covariance matrix into the desired multivariate mixture of normal distributions. The computed covariance matrix is derived analytically. Among the properties of the multivariate mixture of normals that we demonstrate is that any linear combination of mixtures of normal distributions is also a mixture of normal distributions. Methods of fitting mixtures of normal distributions are briefly discussed. A motivating example carried throughout this paper is the use of multivariate mixtures of normals for modeling daily changes in market variables.

A sparse regression and neural network approach for financial factor modeling

Topic models are widely used to discover the latent representation of a set of documents. The two canonical models are latent Dirichlet allocation, and Gaussian latent Dirichlet allocation, where the former uses multinomial distributions over words, and the latter uses multivariate Gaussian distributions over pre-trained word embedding vectors as the latent topic representations, respectively. Compared with latent Dirichlet allocation, Gaussian latent Dirichlet allocation is limited in the sense that it does not capture the polysemy of a word such as "bank." In this paper, we show that Gaussian latent Dirichlet allocation could recover the ability to capture polysemy by introducing a hierarchical structure in the set of topics that the model can use to represent a given document. Our Gaussian hierarchical latent Dirichlet allocation significantly improves polysemy detection compared with Gaussian-based models and provides more parsimonious topic representations compared with hierarchical latent Dirichlet allocation. Our extensive quantitative experiments show that our model also achieves better topic coherence and held-out document predictive accuracy over a wide range of corpus and word embedding vectors which significantly improves the capture of polysemy compared with GLDA and CGTM. Our model learns the underlying topic distribution and hierarchical structure among topics simultaneously, which can be further used to understand the correlation among topics. Moreover, the added flexibility of our model does not necessarily increase the time complexity compared with GLDA and CGTM, which makes our model a good competitor to GLDA.

A financial security represents a prospect to future receipts. The expected value of these receipts will be surrounded with risk. Hence, a financial security can be viewed as a claim on a specific but uncertain pattern of future cash flows, or equivalently as a particular distribution of risky future returns. Future cash flows (and thus the returns) to be received from a financial security will be influenced by economic events or ‘factors’. In this view, when buying a security, an investor is actually buying an exposure to these factors. In a factor model, this exposure is measured in terms of response coefficients or sensitivities of the security’s return for the factor movements. In giving economic content to factor models, one encounters the problems of how to identify and measure the factors (proxies) and how to measure the sensitivities.

It is generally assumed that the likelihood ratio statistic for testing the null hypothesis that data arise from a homoscedastic normal mixture distribution versus the alternative hypothesis that data arise from a heteroscedastic normal mixture distribution has an asymptotic ? 2 reference distribution with degrees of freedom equal to the difference in the number of parameters being estimated under the alternative and null models under some regularity conditions. Simulations show that the ? 2 reference distribution will give a reasonable approximation for the likelihood ratio test only when the sample size is 2000 or more and the mixture components are well separated when the restrictions suggested by Hathaway (Ann. Stat. 13:795---800, 1985) are imposed on the component variances to ensure that the likelihood is bounded under the alternative distribution. For small and medium sample sizes, parametric bootstrap tests appear to work well for determining whether data arise from a normal mixture with equal variances or a normal mixture with unequal variances.

This chapter is a continuation and extension of modern portfolio theory presented in Chapter 3, with an emphasis on risk measures and risk management of a portfolio. It introduces the capital asset pricing model (CAPM), linear factor models, and several approaches to portfolio risk measures such as value-at-risk, conditional value-at-risk and the concept of coherent risk measures, as well as a variety of portfolio evaluation techniques such as the alpha and beta, the Sharpe ratio, the Sortino ratio and maximum drawdown. The introduction to factor models is brief and from intuitive perspective.

This article discusses a modeling framework that links two well‐known statistical methods: structural equation modeling (SEM) and latent class or finite mixture modeling. Mixture SEM can either be viewed as a refinement of multivariate normal (MVN) mixtures, where the within‐class covariance matrices are smoothed according to a postulated SEM structure, or as a form of multiple group SEM, in which the group variable is unobserved. After introducing standard MVN mixtures, it is shown how the SEM framework can be used to restrict the class‐specific means and covariances. Furthermore, parameter estimation, model testing, and software is discussed, and an empirical example is provided.

Purpose: The aim of this study is to investigate the performance of forecasting the South African real spot rate curve using different mathematical term-structure models during the Covid-19 period. This study follows previous studies by Reid (2009) and Mashoene et al., 2021) where dynamic term-structure models performed well compared to static term-structure models over normal market conditions. For high volatility, normality often breaks, which might result in a need for recalibration in the currently used methodology or a total change in the methodology.
 Methodology: This study explores the dynamism of both dynamic term-structure models, which follow the Nelson-Siegel framework, and static term-structure models with the option of recalibration of model parameters to account for a change in macro-economic dynamics brought by the effect of the Covid-19 pandemic. The forecasting exercise was applied to term-structure models following the Nelson-Siegel framework using AR(1) process.
 Findings: The incorporation of macroeconomic factors performed poorly in estimating future model parameters. This could be attributable to the effect of global stress, which resulted in poor linear relationships between macroeconomic and financial factors. Recalibration process on static Nelson-Siegel term-structure models improved the models' performance, especially during the high volatility/period of total economic shutdown due to the Covid-19 pandemic.
 Implications: The application of static Nelson-Siegel term-structure models with recalibrated parameters might improve bond pricing processes and risk management strategies in emerging markets, especially during market stress.

Context reinforced neural topic modeling over short texts

A blind detector for Rayleigh flat-fading channels with non-Gaussian interference via the particle learning algorithm

This article considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model is classical root-T consistent and asymptotically normal when the MA root is inside, outside, and on the unit circle. For more general models where the dependence of the cumulants on the model parameters is analytically intractable, we consider simulation-based estimators with two features. First, in addition to an autoregressive model, new auxiliary regressions that exploit information from the second and higher order moments of the data are considered. Second, the errors used to simulate the model are drawn from a flexible functional form to accommodate a large class of distributions with non-Gaussian features. The proposed simulation estimators are also asymptotically normally distributed without imposing the assumption of invertibility. In the application considered, there is overwhelming evidence of noninvertibility in the Fama-French portfolio returns.

Minimum Distance Estimation of Possibly Non-Invertible Moving Average Models

The Indonesian Government introduced rice farm insurance scheme (Asuransi Usaha Tani Padi – AUTP program) to protect rice farm from loss caused by flood, drought and pest and disease infestations. It has been discussed the method to calculate pure premium of the rice farm insurance scheme in Indonesia with assume that the distribution of rice yield data is normal distribution, gamma distribution, or normal mixture distribution. The normal distribution can be used for the case of distribution of rice yield data in the form of symmetry. The gamma distribution can be used for the case of distribution of rice yield data in the form of skewed to the right or positively skewed. In addition, the normal and gamma distributions are categorized as unimodal distributions. It has also been discussed the method of calculating pure premium of the rice farm insurance scheme in Indonesia with the assumption that the rice yield data is normal mixture distribution. The normal mixture distribution can be categorized as multimodal distribution. Characteristic of the normal mixture distribution is suitable for rice yield data in Indonesia that contain rice yield data from several provinces. On the other hand it is also known that the 4-parameter beta mixture distribution can be applied to rice yield data in Indonesia. This distribution is more flexible than the normal mixture distribution in terms of the tail shape of the distribution. In this paper, pure premium calculation method of the AUTP program is formulated with assume that the distribution of rice yield data is the 4-parameter beta mixture distribution.Monte Carlo simulation is used to evaluate performance of the method. The Monte Carlo simulation results show that the proposed method has higher accuracy and precision when increasing sample size. The method is applied to the rice productivity data in several provinces in Indonesia for the period 1970 to 2016.

<div class="section abstract"><div class="htmlview paragraph">An essential step in predicting the output of a complicated system is the calibration of model parameters, but this step cannot be conducted directly if the data at the system-level are not available. In such a situation, a reasonable route is to quantify the system model parameters using tests at lower levels of complexity which share the same model parameters with the system, and propagate the results through the computational model at the system level. For such a multi-level problem, this paper proposes a methodology to quantify the uncertainty in the system-level model parameters by integrating model calibration, model validation and sensitivity analysis at different levels. The proposed approach considers the validity of the models used for parameter estimation at lower levels, as well as the relevance at the lower level to the prediction at the system level. The model validity is evaluated using a model reliability metric, which is extended to handle the uncertainty in model validity and models with multivariate output. The relevance is quantified by comparing Sobol indices at the lower level and system level, thus measuring the extent to which a lower level test represents the characteristics of the actual system so that the calibration results can be reliably used in the system level. Finally a roll-up method is proposed to integrate the results of calibration, validation and relevance analysis and predict the system output.</div></div>