Econophysics and Data Driven Modelling of Market Dynamics by Frédéric Abergel, Hideaki Aoyama, Bikas K. Chakrabarti,

By Frédéric Abergel, Hideaki Aoyama, Bikas K. Chakrabarti, Anirban Chakraborti, Asim Ghosh

This publication offers the works and study findings of physicists, economists, mathematicians, statisticians, and monetary engineers who've undertaken data-driven modelling of marketplace dynamics and different empirical experiences within the box of Econophysics. in the course of fresh a long time, the monetary marketplace panorama has replaced dramatically with the deregulation of markets and the starting to be complexity of goods. The ever-increasing pace and lowering expenditures of computational energy and networks have ended in the emergence of massive databases. the provision of those info should still let the advance of types which are greater based empirically, and econophysicists have for that reason been advocating that one may still count totally on the empirical observations which will build versions and validate them. the hot turmoil in monetary markets and the 2008 crash seem to supply a robust motive for brand spanking new versions and methods. The Econophysics neighborhood consequently has a tremendous destiny function to play in marketplace modelling. The Econophys-Kolkata VIII convention court cases are dedicated to the presentation of many such modelling efforts and handle fresh advancements. a few prime researchers from around the globe document on their contemporary paintings, touch upon the newest concerns, and evaluate the modern literature.

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Notice that, when increasing the λR , the bias increases and the variance decreases. On the other hand, when decreasing the λR , the bias decreases and the variance increases converging to their OLS values. To enhance the stability of the linear regression, one should compute a λR , such that MSE(βR ) ≤ MSE(β). As proved by Hoerl [15], this is always possible. Theorem: There always exist λR ≥ 0 such that MSE(βR ) ≤ MSE(β). From a statistical view, adding the Ridge penalty aims to reduce the MSE of the estimator, and is particularly necessary when the covariance matrix is ill-conditioned.

Notice that, when increasing the λR , the bias increases and the variance decreases. On the other hand, when decreasing the λR , the bias decreases and the variance increases converging to their OLS values. To enhance the stability of the linear regression, one should compute a λR , such that MSE(βR ) ≤ MSE(β). As proved by Hoerl [15], this is always possible. Theorem: There always exist λR ≥ 0 such that MSE(βR ) ≤ MSE(β). From a statistical view, adding the Ridge penalty aims to reduce the MSE of the estimator, and is particularly necessary when the covariance matrix is ill-conditioned.

The LASSO method [18] enhances the conditioning of the covariance matrix by reducing the number of the used indicators. e. with some coefficients exactly equal to 0. This is possible thanks to the l1 -penalization. ||1 denotes the l1 -norm, defined as the sum of the coordinates’ absolute values. Writing |βi | = βi+ − βi− and βi = βi+ + βi− , with βi+ ≥ 0 and βi− ≤ 0, a classic quadratic problem, with a linear constraints, is obtained and can be solved by a classic solver. As far as known, there is no estimator for λL .

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