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Count Time-Series Analysis: A Signal Processing Perspective

机译：计数时间序列分析：信号处理透视

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Signal processing techniques are constantly expanding to accommodate a wider range of data structures and applications. A time series is a sequence of observations taken sequentially in time. Time-series analysis is concerned with techniques for the analysis of serial dependence and their use in practical applications, including 1) forecasting of future values from current and past values and 2) outlier detection and intervention analysis. Traditionally, time-series analysis has been applied to continuously varying data. However, in many areas of science and engineering we encounter count variables, i.e., variables that take on nonnegative integer values. Time series of counts are obtained in various disciplines whenever many events are counted during certain time periods. Examples include the monthly number of car accidents in a region, the weekly number of new cases in epidemiology, the number of transactions at a stock market per minute in finance, or the number of photon arrivals per microsecond in a focal-plane array. In some cases, the counts are large numbers and it makes sense to approximate them by continuous variables. However, there are many applications where the counts tend to be small and include many zeros. In this case, the observations cannot be adequately modeled with a continuous distribution. During the last three decades, there has been significant progress in the area of count time-series analysis [1], [2]. The main objective of this article is to present the state-of-the-art developments for modeling count time series in a signal processing framework by emphasizing the key theoretical, methodological, and practical application issues.
机译：信号处理技术不断扩展以适应更广泛的数据结构和应用。时间序列是一系列观察序列依次采取。时间序列分析涉及用于分析串行依赖性及其在实际应用中的使用的技术，包括1）预测来自电流和过去的价值的未来价值，2）个异常检测和干预分析。传统上，时间序列分析已应用于连续变化的数据。但是，在许多科学和工程领域，我们遇到计数变量，即取决于非负整数值的变量。每当在某些时间段期间计算许多事件时，在各种学科中获得了时间序列。示例包括一个地区的每月汽车事故的数量，流行病学的每周新案例数，金融中每分钟的股票市场交易数量，或者在焦平面阵列中每微秒的光子到达数量。在某些情况下，计数是大量的，并且通过连续变量近似有意义。然而，有许多应用程序的计数往往小并且包括许多零。在这种情况下，观察结果不能用连续分布进行充分建模。在过去的三十年中，计数时间序列分析[1]，[2]的数量方面存在显着进展。本文主要目的是通过强调关键理论，方法论和实际应用问题，提出用于建模计数时间序列的最先进的开发。

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