英文标题：
《Learning from the past, predicting the statistics for the future,
  learning an evolving system》
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作者：
Daniel Levin, Terry Lyons and Hao Ni
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最新提交年份：
2016
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英文摘要：
  We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a stream.   A certain graded feature set of a stream, known in the rough path literature as the signature, has a universality that allows formally, linear regression to be used to characterise the functional relationship between independent explanatory variables and the conditional distribution of the dependent response.   This approach, via linear regression on the signature of the stream, is almost totally general, and yet it still allows explicit computation. The grading allows truncation of the feature set and so leads to an efficient local description for streams (rough paths). In the statistical context this method offers potentially significant, even transformational dimension reduction.   By way of illustration, our approach is applied to stationary time series including the familiar AR model and ARCH model. In the numerical examples we examined, our predictions achieve similar accuracy to the Gaussian Process (GP) approach with much lower computational cost especially when the sample size is large.
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中文摘要：
我们将粗糙路径理论引入到流数据的非参数统计研究中。我们讨论回归问题，其中输入变量是一个信息流，依赖响应也是（潜在的）一个流。流的某个分级特征集（在粗糙路径文献中称为签名）具有普遍性，允许使用形式上的线性回归来描述独立解释变量和相关响应的条件分布之间的函数关系。这种方法，通过对流的特征进行线性回归，几乎是完全通用的，但它仍然允许显式计算。分级允许截断特征集，因此可以对流（粗糙路径）进行有效的局部描述。即使在这种情况下，统计方法也可能提供显著的转换维度。通过举例说明，我们的方法被应用于平稳时间序列，包括熟悉的AR模型和ARCH模型。在我们研究的数值例子中，我们的预测达到了与高斯过程（GP）方法相似的精度，但计算成本要低得多，尤其是当样本量较大时。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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