By Frédéric Abergel, Hideaki Aoyama, Bikas K. Chakrabarti, Anirban Chakraborti, Asim Ghosh
This e-book provides the works and study findings of physicists, economists, mathematicians, statisticians, and fiscal engineers who've undertaken data-driven modelling of industry dynamics and different empirical stories within the box of Econophysics. in the course of contemporary a long time, the monetary industry panorama has replaced dramatically with the deregulation of markets and the turning out to be complexity of goods. The ever-increasing velocity and reducing expenditures of computational strength and networks have resulted in the emergence of massive databases. the supply of those info may still enable the improvement of versions which are higher based empirically, and econophysicists have therefore been advocating that one may still count totally on the empirical observations in an effort to build types and validate them. the new turmoil in monetary markets and the 2008 crash seem to provide a robust purpose for brand new types and techniques. The Econophysics group as a result has a massive destiny position to play in marketplace modelling. The Econophys-Kolkata VIII convention court cases are dedicated to the presentation of many such modelling efforts and deal with fresh advancements. a couple of best researchers from around the globe document on their contemporary paintings, touch upon the newest matters, and evaluate the modern literature.
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Additional info for Econophysics and Data Driven Modelling of Market Dynamics
In particular, the condition number is higher than 80,000. This finding explains the instability observed on the previous section. Moreover that the OLS estimator is statistically not satisfactory, the numerical problems due to the ill-conditioning of the matrix makes the result numerically unreliable. One popular solution to enhance the stability of the estimation of the regression coefficients is the Ridge method. This method was introduced independently by A. E. Hoerl in the context of addressing the linear regression problems by the sixteeth.
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 , 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.
Figure 16 shows that the coefficients obtained by the EN method are in line with the financial view and combine both regularization effects observed when using the Ridge and the LASSO methods. 2 (trading only if Y ≥ |θ | ) is applied to the different regression methods. Figure 17 summarizes the obtained results. Empirical Evidence of Market Inefficiency: Predicting Single-Stock Returns 23 Fig. 16 The quality of the EN prediction: the graphs show that the EN regression gives a regression coefficients in line with the financial view (similarly to Figs.