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Retrodicting with the truncated Lévy flight
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2022-09-24 , DOI: 10.1016/j.cnsns.2022.106900
Raul Matsushita, Pedro Brom, Mateus Nagata, Sergio Da Silva

There is a point in predicting the past (retrodicting) because we lack information about it. To address this issue, we consider a truncated Lévy flight to model data. We build on the finding that there is a power law between truncation length and standard deviation that connects the bounded past and unbounded future. Even if a truncated Lévy flight cannot predict future extreme events, we argue that it can still be used to model the past. Because we avoid the exact form of the probability density function while allowing its distributional moments, with the exception of the mean, to vary over time, our method is applicable to a wide range of symmetric distributions. We illustrate our point by using US dollar prices in 15 different currencies traded on foreign exchange markets.



中文翻译:

使用截断的 Lévy 航班进行追溯

预测过去(追溯)是有道理的,因为我们缺乏关于它的信息。为了解决这个问题,我们考虑使用截断的 Lévy 飞行来建模数据。我们建立在以下发现的基础上:截断长度和标准差之间存在幂律,连接有界的过去和无界的未来。即使截断的 Lévy 飞行无法预测未来的极端事件,我们认为它仍然可以用来模拟过去。因为我们避免了概率密度函数的精确形式,同时允许其分布矩(均值除外)随时间变化,所以我们的方法适用于广泛的对称分布。我们通过使用在外汇市场交易的 15 种不同货币的美元价格来说明我们的观点。

更新日期:2022-09-24
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