菲利普斯曲线的Mittag-Leffler拟合

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摘要翻译：
本文首次提出了一个基于单参数Mittag-Leffler函数的数学模型，即菲利普斯曲线来描述失业率与通货膨胀率之间的关系。菲利普斯曲线在文献中常以指数形状表示。另一方面，Phillips在他的基础论文中在模型定义中使用了幂函数。考虑到普通和推广的Mittag-Leffler函数介于纯指数函数和幂函数之间，在描述表示菲利普斯曲线的数据之间关系的模型定义中实现它是很自然的。为了建模目的，使用了法国和瑞士这两个不同的欧洲经济体的数据，并进行了“样本外”预测，将Mittag-Leffler模型的性能与幂型和指数型模型的性能进行了比较。结果表明，Mittag-Leffler函数拟合表现为伸展指数、振荡甚至阻尼振荡迹象的数据的能力在描述经济关系和现象（如菲利普斯曲线）时是有用的。
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英文标题：
《The Mittag-Leffler Fitting of the Phillips Curve》
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作者：
Tomas Skovranek
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最新提交年份：
2019
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分类信息：

一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
--

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英文摘要：
  In this paper, a mathematical model based on the one-parameter Mittag-Leffler function is proposed to be used for the first time to describe the relation between unemployment rate and inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a power function in the model definition. Considering that the ordinary as well as generalised Mittag-Leffler function behaves between a purely exponential function and a power function it is natural to implement it in the definition of the model used to describe the relation between the data representing the Phillips curve. For the modelling purposes the data of two different European economies, France and Switzerland, were used and an "out-of-sample" forecast was done to compare the performance of the Mittag-Leffler model to the performance of the power-type and exponential-type model. The results demonstrate that the ability of the Mittag-Leffler function to fit data that manifest signs of stretched exponentials, oscillations or even damped oscillations can be of use when describing economic relations and phenomenons, such as the Phillips curve.
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PDF链接：
https://arxiv.org/pdf/1604.00369

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关键词：菲利普斯曲线 菲利普斯 tag MIT ITT between 指数 振荡 relation 使用