"Market making" behaviour in an order book model and its impact on the bid-ask spread

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.Comment: 17 pages, 9 figure

Why Biology is Beyond Physical Sciences?

In the framework of materialism, the major attention is to find general organizational laws stimulated by physical sciences, ignoring the uniqueness of Life. The main goal of materialism is to reduce consciousness to natural processes, which in turn can be translated into the language of math, physics and chemistry. Following this approach, scientists have made several attempts to deny the living organism of its veracity as an immortal soul, in favor of genes, molecules, atoms and so on. However, advancement in various fields of biology has repeatedly given rise to questions against such a denial and has supplied more and more evidence against the completely misleading ideological imposition that living entities are particular states of matter. In the recent past, however, the realization has arisen that cognitive nature of life at all levels has begun presenting significant challenges to the views of materialism in biology and has created a more receptive environment for the soul hypothesis. Therefore, instead of adjudicating different aprioristic claims, the development of an authentic theory of biology needs both proper scientific knowledge and the appropriate tools of philosophical analysis of life. In a recently published paper the first author of present essay made an attempt to highlight a few relevant developments supporting a sentient view of life in scientific research, which has caused a paradigm shift in our understanding of life and its origin [1]. The present essay highlights the uniqueness of biological systems that offers a considerable challenge to the mainstream materialism in biology and proposes the Vedāntic philosophical view as a viable alternative for development of a biological theory worthy of life

"Selection of Variables in Multivariate Regression Models for Large Dimensions"

The Akaike information criterion, AIC, and Mallows' Cp statistic have been proposed for selecting a smaller number of regressor variables in the multivariate regression models with fully unknown covariance matrix. All these criteria are, however, based on the implicit assumption that the sample size is substantially larger than the dimension of the covariance matrix. To obtain a stable estimator of the covariance matrix, it is required that the dimension of the covariance matrix be much smaller than the sample size. When the dimension is close to the sample size, it is necessary to use ridge type of estimators for the covariance matrix. In this paper, we use a ridge type of estimators for the covariance matrix and obtain the modified AIC and modified Cp statistic under the asymptotic theory that both the sample size and the dimension go to infinity. It is numerically shown that these modified procedures perform very well in the sense of selecting the true model in large dimensional cases.

Exact and asymptotic solutions of the call auction problem

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.Comment: 24 pages, 7 figure

Magnetic island merger as a mechanism for inverse magnetic energy transfer

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: magnetic energy decays as $\tilde t^{-1}$, where $\tilde t$ is time normalized to the (appropriately defined) reconnection timescale; and the correlation length of the field grows as $\tilde t^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto \tilde t ^{-3/2}k^{-2}$, where the $k$-dependence is imparted by the formation of thin current sheets.Comment: 6 pages, 5 figures, submitted for publicatio

Coastal upwelling along the southwest coast of India ? ENSO modulation

International audienceAn index of El Niño Southern Oscillation (ENSO) in the Pacific during pre monsoon is shown to account for a significant part of the variability of coastal Sea Surface Temperature (SST) anomalies measured a few months later within the wind driven southwest coast of India coastal upwelling region 7° N?14° N. This teleconnection is thought to result from an atmospheric bridge between the Pacific and north Indian Oceans, leading to warm (cold) ENSO events being associated with relaxation (intensification) of the Indian trade winds and of the wind-induced coastal upwelling. This ENSO related modulation of the wind-driven coastal upwelling appears to contribute to the connection observed at the basin-scale between ENSO and SST in the Arabian Sea. The ability to use this teleconnection to give warning of large changes in the southwest coast of India coastal upwelling few months in advance is successfully tested using data from 1998 and 1999 ENSO events

"Tests for Multivariate Analysis of Variance in High Dimension Under Non-Normality"

In this article, we consider the problem of testing the equality of mean vectors of dimension ρ of several groups with a common unknown non-singular covariance matrix Σ, based on N independent observation vectors where N may be less than the dimension ρ. This problem, known in the literature as the Multivariate Analysis of variance (MANOVA) in high-dimension has recently been considered in the statistical literature by Srivastava and Fujikoshi[7], Srivastava [5] and Schott[3]. All these tests are not invariant under the change of units of measurements. On the lines of Srivastava and Du[8] and Srivastava[6], we propose a test that has the above invariance property. The null and the non-null distributions are derived under the assumption that ( N, ρ) → ∞ and N may be less than ρ and the observation vectors follow a general non-normal model.