{'fraction_non_alphanumeric': 0.025200458190148912, 'fraction_numerical': 0.002290950744558992, 'mean_word_length': 5.173144876325089, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Count Time-Series Analysis: A Signal Processing Perspective

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.