论文标题
等价关系和时间序列之间的$ l^p $距离与黑色夏季澳大利亚丛林
Equivalence relations and $L^p$ distances between time series with application to the Black Summer Australian bushfires
论文作者
论文摘要
本文介绍了时间序列与新距离指标之间的代数等效关系的新框架，然后将其应用于2019-2020的澳大利亚``黑人夏季''灌木丛季节。首先，我们介绍了一个通用框架，用于定义时间序列之间的等效性，如果它们仅与噪声相差，则启发式意图是等效的。我们的第一个特定实现是基于使用变更点算法并比较统计段中平均值或差异等统计量的基础。因此，我们在时间序列的时间序列上得出了这种对等关系的存在，因此商空间可以配备可衡量的拓扑。接下来，我们专门说明了如何在时间序列的集合中定义和计算此类距离，并执行聚类和其他分析。然后，我们将这些见解应用于2019 - 2020年灌木丛期间分析澳大利亚新南威尔士州的空气质量数据。在那里，我们研究了相对于此数据的结构相似性，并确定了受火灾相对于其位置匿名影响的位置。这可能对适当管理的资源管理有影响，以避免防御未来火灾的差距。
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.
