时间序列之间的等价关系和$L^p$距离及其在澳大利亚黑夏山火中的应用
Equivalence relations and $L^p$ distances between time series with application to the Black Summer Australian bushfires
摘要：
本文介绍了一种新的时间序列之间的代数等价关系框架和它们之间的新距离度量，然后应用这些来研究2019-2020年澳大利亚“黑色夏天”的山火季节。首先，我们介绍了一个一般的框架定义之间的等价时间序列，简明地打算是等价的，如果他们不同的噪音。我们的第一个具体实现是基于使用变点算法和比较统计量，如平均值或方差在固定段。由此我们得到了在时间序列空间上存在这样的等价关系，使得商空间可以具有可度量化的拓扑。接下来，我们具体说明如何定义和计算时间序列的集合之间的这种距离，并对其执行聚类和附加分析。然后，我们将这些见解应用于分析2019-2020年澳大利亚新南威尔士州的空气质量数据。在那里，我们调查了这些数据的结构相似性，并确定了相对于其位置受到火灾匿名影响的位置。这可能会对资源的适当管理产生影响，以避免未来火灾的防御缺口。
英文摘要：
This paper introduces a new framework of algebraic equivalence relations between time series and new distance metrics between them, then applies these to investigate the Australian ``Black Summer'' bushfire season of 2019-2020. First, we introduce a general framework for defining equivalence between time series, heuristically intended to be equivalent if they differ only up to noise. Our first specific implementation is based on using change point algorithms and comparing statistical quantities such as mean or variance in stationary segments. We thus derive the existence of such equivalence relations on the space of time series, such that the quotient spaces can be equipped with a metrizable topology. Next, we illustrate specifically how to define and compute such distances among a collection of time series and perform clustering and additional analysis thereon. Then, we apply these insights to analyze air quality data across New South Wales, Australia, during the 2019-2020 bushfires. There, we investigate structural similarity with respect to this data and identify locations that were impacted anonymously by the fires relative to their location. This may have implications regarding the appropriate management of resources to avoid gaps in the defense against future fires.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
