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|Title:||Stochastic Market Modeling with Gaussian Quadratures: Do Rotations of Stroud's Octahedron Matter?|
|Authors:||ARTAVIA OREAMUNO MARCO ANTONIO; GRETHE Harald; ZIMMERMANN Georg|
|Citation:||ECONOMIC MODELLING vol. 45 p. 155-168|
|Publisher:||ELSEVIER SCIENCE BV|
|Type:||Articles in periodicals and books|
|Abstract:||Recently, stochastic applications of large-scale applied simulation models of agricultural markets have become more common. However, stochastic modeling with large market models incurs high computational and management costs for data storage, analysis and manipulation. Gaussian Quadratures (GQ) are efficient sampling methods requiring few points to approximate the central moments of the joint probability distribution of stochastic variables, thereby reducing computational costs. For symmetric regions of integration, the vertices of Stroud's n-octahedron (Stroud 1957) are GQ formulas of degree 3 with a minimal number of points which can make stochastic modeling with large economic models manageable. However, the conjecture exits that rotations of Stroud's n-octahedron may have an effect on the accuracy of approximation of the model results. To address this, eight different rotations (quadrature formulas) were tested using the European Simulation Model (ESIM). It was found that formulas employing 0° and 45° rotation are crucial, and furthermore, that the formulas based on 45° rotation yield higher accuracy. With the formulas based on 45° rotation and in models or markets with high asymmetries, as is the case for soft wheat, the arrangement of the stochastic variables in the covariance matrix or the method selected to induce the covariance may have a significant effect on the accuracy of the quadratures. With the formulas based on 45° rotation and with less market asymmetry, as is the case for rapeseed, the stochastic variable arrangement and the method to induce the covariance might not have a significant impact on the accuracy of the quadratures.|
|JRC Directorate:||Growth and Innovation|
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