Derivation of the Wishart distribution of the second order sample moments by straightforward integration of a multiple integral

1. Introduction.

In his textbook of statistics Kendall classifies the methods of deducing exact sampling distributions into four groups:

• (a) straightforward evaluation of the integral in question by ordinary analytical processes such as a convenient change of variable;

• (b) the use of geometrical terminology;

• (c) the use of characteristic functions; and

• (d) other analytical methods.

     

On distributions of functions of samples from a normally distributed infinite population

Abstract

7. The joint distribution of the moments a ₁₁, a ₂₂,…, a_nn and a ₁₂, …, a _1n may be deduced explicitly in the case, in which the variates χ₁, …, χ _n in (1) are mutually uncorrelated. In this case we have for the population values of the moments: α_μv = 0 for μ ═ v and, consequently, A_μv = 0 for μ ═ v, so that according to (6) λ_μv = 0 for μ ═ v; the distribution (5) of the moments α_μv is then      

On distributions of functions of samples from a normally distributed infinite population

Abstract

1. The theory of the distributions of functions of samples from a normally distributed infinite population has in recent years developed considerably, so as to comprise at present an extensive aggregate of well known distributions of functions of samples used in the practical applications of theoretical statistics, e.g. regression coefficients, total, partial and multiple correlation coefficients, total and partial standard deviations, and so on.     

The role of volume in order book dynamics: a multivariate Hawkes process analysis

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.     

The impact of the COVID-19 pandemic and Russia-Ukraine war on multiscale spillovers in green finance markets: Evidence from lower and higher order moments

This study analyzes the impact of the COVID-19 pandemic and the Russia-Ukraine war on the connectedness of lower-order moments (returns and volatility) and higher-order moments (skewness and kurtosis) in the markets of green bonds, clean energy, wind, solar, and sustainability indexes. To compare the spillover effects of these moments, we use the Diebold and Yilmaz and Barunik and Krehlik methods. Our findings show that the total spillover effect of lower-order moments is higher than that of higher-order moments in the time domain. In the frequency domain, the total return and skewness spillover are primarily concentrated in the short term, whereas the total volatility spillover is mainly concentrated in the long term. Furthermore, we observe that the spillover effect of the Russia-Ukraine war on the green finance market is mild, while the COVID-19 pandemic has a significant and unprecedented influence on the spillover of both lower- and higher-order moments in this market. Additionally, we note that before the COVID-19 outbreak, the total kurtosis spillover was irregular, but it became concentrated in the long term after the outbreak. Moreover, the continuation of COVID-19 has had an unprecedented and long-lasting impact on the kurtosis and skewness of the green bond market.     

Exemptions from first semester accounting and performance in the second semester course: an emperical study

This study investigates the impact on second semester results of an exemption from first semester university accounting. It is concluded that, prividing students have achieved an ‘A’ in high school accounting, they will not be disadvantaged if they do not undertake first semester accounting.     

The regression problem involving non-random variates in the case of stratified sample from normal parent populations with varying regression coefficients

Abstract

1. Introduction.

A sample of N independently observed points (x_{o 1} | x₁₁ , x₂₁ ,... , x_pt ), i = 1, 2, ... , N≥ p is given, where xk, k = 1, 2, ... , p are known, possibly choosable, non-random variates. Suppose now that, for any fixed values of x₁ , x₂ ..., x_p the random variable _o is normally distributed with the mean and the variance λ_o α _x and λ_o are unknown parameters, not involving xk, the regression coefficients and the residual variance of the parent population respectively.     

Bayesian multivariate regime-switching models and the impact of correlation structure misspecification in variable annuity pricing

ABSTRACT

We develop Bayesian multivariate regime-switching models for correlated assets, comparing three different ways to flexibly structure the correlation matrix. After developing the models, we examine their relative characteristics and performance, first in a straightforward asset simulation example, and later applied to a variable annuity product with guarantees. We find that the freedom allowed by the more flexible structures enables these models to more accurately reflect the actual asset dependence structure. We also show that the correlation structures inferred by the most commonly used (and simplest) model will result in significantly larger estimates of the cost of the annuity guarantees.     

Discrete devaluations and multiple equilibria in a first generation model of currency crises

The first generation models of currency crises have often been criticized because they predict that, in the absence of very large triggering shocks, currency attacks should be predictable and lead to small devaluations. This paper shows that these features of first generation models are not robust to the inclusion of private information. In particular, this paper analyzes a generalization of the Krugman-Flood-Garber (KFG) model, which relaxes the assumption that all consumers are perfectly informed about the level of fundamentals. In this environment, the KFG equilibrium of zero devaluation is only one of many possible equilibria. In all the other equilibria, the lack of perfect information delays the attack on the currency past the point at which the shadow exchange rate equals the peg, giving rise to unpredictable and discrete devaluations.     

Study on the effect of sample size on type I error,in the first,second and first-two digits excessmad tests

The first-two digits ExcessMAD test was created in 2016, allowing to evaluate whether a certain data set conforms to Benford’s Law (BL). The purpose of this study is to explore some questions that remained open: develop the exact and approximate mathematical formulation of the first and second digit ExcessMAD test and study the type I error of these tests when applied to different sample sizes conforming to BL and to the uniform distribution, due to its wide use in accounting data. The importance of this study is to make available to accountants, auditors and researchers the first and second digit ExcessMAD tests, which will make it possible to conduct further investigations involving BL, especially for smaller samples. In addition, the relevance of the type I error analysis stems from the reduction of unnecessary additional studies for the investigation of non-conformity, in the case of the erroneous rejection of the null hypothesis stated as conforming to BL. The application of the second digit ExcessMAD test in the uniform distribution reveals that the close proximity between the uniform and BL distributions can lead to misinterpretations. Based on the exact and approximate mathematical formulations of the three ExcessMAD tests and the use of the Monte Carlo simulation technique, samples were generated in accordance with the BL and uniform distributions, with sizes between 100 and 3,500 elements, which allowed the study of type I error and the comparison of the tests applied to those distributions. This paper seeks to cover three gaps in the literature on ExcessMAD tests. In the previous studies, the following approaches were not found: the exact and approximate mathematical formulation of the first and second digit ExcessMAD tests; the analysis of type I error in these tests and the comparison of such results in the BL and Uniform distributions.     

The effectiveness of incorporating higher moments in portfolio strategies: evidence from the Chinese commodity futures markets

This paper examines portfolio strategies that incorporate individual and systematic higher-order moments, within a stochastic optimization framework with uncertain mean and covariance. Using weekly, daily, and 30-minute interval data on Chinese commodity futures, we show that incorporating higher moments into portfolio strategies generally leads to better performance. The systematic fourth-order moment, among all systematic moments considered, can lead to the most robust, and a relatively large, improvement in investment performance, while the contribution of individual moments to the improved performance depends on the data horizon. We also find that adding higher moments brings superior performance in more cases for 30-minute-interval data than for other low-frequency data, suggesting that our strategy most likely performs best in 30-minute-rebalancing investments.     

The dynamics in the spot,futures, and call options with basis asymmetries: an intraday analysis in a generalized multivariate GARCH-M MSKST framework

The main purpose of the study is to explore the dynamic relationship among the TAIEX spot, futures, and options markets by proposing an innovative multivariable GARCH-M MSKST (Multivariate Skewed-Student distribution) model. In addition to the considerable feedback effects of these three markets in terms of return transmissions, a significant bidirectional relationship is also found in volatility transmissions between futures and spot markets, and unidirectional spillover occurs from futures to options markets. Specifically, futures are found to exert the most influence on spot and options, and play an important role in disclosing information and pricing discovery to the other two markets. Comparing the magnitude of the effect the positive and negative basis has on spot prices, it is evident that positive basis has a greater impact on the spot market than negative basis does. Of interest, our study shows that positive basis has even more effect than negative basis does on the conditional variance of return on spot and futures.

The probability of decrements from a population. A study in discrete random processes

Abstract

The statistician, whether he be biologist, actuary, or worker III the social sciences, often requires to measure the intensity of some decremental force, or forces, acting on an observed body of individuals. The latter may be human beings, animals, or even inanimate objects (e. g. aircraft), and the decrements considered may range from marriage to‘write-off’. N evertheless the assumptions made are, for the most part, analogous and the technique adopted is broadly the same in every case: the decrements are assumed to be random (in the technical sense) and they are related to the body in which they have occurred (the so-called‘exposed to risk’) in order to obtain a relative frequency, or‘rate’, of decrement.     

The value of control: Evidence from full and partial acquisitions in the real estate industry

We investigate the differential wealth effects of (1) full and partial control acquisitions, (2) nonreal estate, real estate and REIT participants, and (3) single- and multiple-bidder events. We find that target firms earn positive excess returns at the announcement of partial and full acquisitions, but acquisitions that result in control earn larger excess returns than noncontrol acquisitions. An examination of industry differences shows that real estate firms or REITs do not earn higher returns relative to nonreal estate firms. Our analysis of market structure finds that bidders that are not involved in an acquisition program earn greater announcement period returns than prior acquirers. For target firms, we find that those with a single offer earn higher returns than those with subsequent offers. A cross-sectional regression analysis shows that while market structure is important in explaining returns, the main determining factor for target firms is the degree of control sought.     

The decision to first enter the public bond market: The role of firm reputation,funding choices,and bank relationships

This paper uses survival analysis to investigate the timing of a firm’s decision to issue for the first time in the public bond market. We find that firms that are more creditworthy and have higher demand for external funds issue their first public bond earlier. We also find that issuing private bonds or taking out syndicated loans is associated with a faster entry to the public bond market. According to our results, the relationships that firms develop with investment banks in connection with their private bond issues and syndicated loans further speed up their entry to the public bond market. Finally, we find that a firm’s reputation has a “U-shaped” effect on the timing of a firm’s bond IPO. Consistent with Diamond’s reputational theory, firms that establish a track record of high creditworthiness as well as those that establish a track record of low creditworthiness enter the public bond market earlier than firms with intermediate reputation.     

The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics

This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are essential in capturing the volatility smirk effects observed in short-term options.

The non mortality of hypertrophic cardiomyopathy in an unselected, community diagnosed and treated population

Hypertrophic Cardiomyopathy (HC) is portrayed in past literature as having an ominous prognosis. However, most studies emanated from medical centers and suffered from potential referral bias. A population based, community diagnosed and treated survival study is analyzed by the life table method. Despite potential causes for both underestimation of the observed mortality as well as for overestimation of expected mortality, the study appears to reveal a more favorable prognosis for HC in this population.     

The birth of a nation: Accounting and Canada’s first nations, 1860–1900

The 1860–1900 period was both the “birth” of Canada but also the birth and institutionalization of a specific set of social relations between the federal government and First Nations peoples. This study examines the roles played by accounting and funding relations within the process of nation building. Throughout this formative period in Canada’s history, governance was attempted via the introduction of financial legislation and enacted by the Indian Department and agents in the field. As our analysis highlights, legislative initiatives, Indian Department pronouncements and the activities of agents imposed, enlisted and implied a variety of accounting technologies. This study not only explores how the federal government has used accounting/funding mechanisms in the attempt to translate government policy regarding indigenous peoples into practice but also provides a history of the present by examining the historical consequences of these interventions.