论文标题
多维和非平稳的最大熵原理的计算量表稀疏公式
On a computationally-scalable sparse formulation of the multidimensional and non-stationary maximum entropy principle
论文作者
论文摘要
基于最大熵原理（Maxent-Principle）的数据驱动的建模和计算预测旨在查找可简单的可能性 - 但不是更简单的必要模型 - 允许避免数据过度拟合问题的模型。我们得出了Maxent原理的多元非参数和非平稳配方，并表明可以通过正则化的稀疏约束优化问题的数值最大化来近似其解决方案。所得算法在流行的财务基准中的应用揭示了无内存的模型，允许对主要股票市场索引数据进行简单和定性的描述。我们将所获得的最大模型与来自计算计量经济学（Garch，Garch-GJR，MS-GARCH，GARCH-PML4）的异质模型进行了比较。我们比较所得的模型日志样式，贝叶斯信息标准的值，后验模型概率，数据自相关函数的质量拟合以及价值风险的预测质量。我们表明，所有考虑的七个主要金融基准时间序列（DJI，SPX，FTSE，STOXX，SMI，HSI和N225）通过有条件的无内存的Maxent模型更好地描述了与具有有限记忆的通用计量经济学模型相比，具有非机构经济性的示例。该分析还揭示了一个稀疏的统计学上重要的时间关系网络，以实现不同市场之间的积极和负面差异变化。为开放访问提供了代码。
Data-driven modelling and computational predictions based on maximum entropy principle (MaxEnt-principle) aim at finding as-simple-as-possible - but not simpler then necessary - models that allow to avoid the data overfitting problem. We derive a multivariate non-parametric and non-stationary formulation of the MaxEnt-principle and show that its solution can be approximated through a numerical maximisation of the sparse constrained optimization problem with regularization. Application of the resulting algorithm to popular financial benchmarks reveals memoryless models allowing for simple and qualitative descriptions of the major stock market indexes data. We compare the obtained MaxEnt-models to the heteroschedastic models from the computational econometrics (GARCH, GARCH-GJR, MS-GARCH, GARCH-PML4) in terms of the model fit, complexity and prediction quality. We compare the resulting model log-likelihoods, the values of the Bayesian Information Criterion, posterior model probabilities, the quality of the data autocorrelation function fits as well as the Value-at-Risk prediction quality. We show that all of the considered seven major financial benchmark time series (DJI, SPX, FTSE, STOXX, SMI, HSI and N225) are better described by conditionally memoryless MaxEnt-models with nonstationary regime-switching than by the common econometric models with finite memory. This analysis also reveals a sparse network of statistically-significant temporal relations for the positive and negative latent variance changes among different markets. The code is provided for open access.
