Changepoints are essential for homogenizing categorical time series and analyzing their trends and variations. The original total cloud cover in Canada was recorded hourly in tenths (or eighths), exhibiting inherent seasonality and serial correlation. Lu and Wang (2012) introduced an extended cumulative logit model to detect shifts in the annual frequencies of cloud cover conditions. While annual aggregation mitigates seasonality and serial correlation, it shortens the time series and may lead to overdispersion. This article introduces a marginalized transition model to detect a single changepoint in periodic and serially correlated categorical time series. The model captures serial dependence using a first-order Markov chain and enables category-specific changepoint specification. To enhance computational efficiency, we develop a new parameter estimation procedure for obtaining maximum likelihood estimates. A maximally selected likelihood ratio test statistic is then proposed to test for sudden changes in categorical time series, and the method is illustrated using daily total cloud cover observations recorded at 9 a.m. and 3 p.m. at Fort St. John Airport, British Columbia, Canada.

翻译：变点对于均一化分类时间序列及分析其趋势与变异至关重要。加拿大原始总云量数据以十分（或八分）制每小时记录一次，呈现固有季节性和序列相关性。Lu与Wang（2012）引入扩展累积logit模型以检测云量条件年频率的偏移。尽管年聚合可削弱季节性与序列相关性，但会缩短时间序列并可能导致过度离散。本文提出一种边缘化转移模型，用于检测具有周期性和序列相关性的分类时间序列中的单一变点。该模型通过一阶马尔可夫链捕捉序列依赖性，并允许按类别指定变点。为提升计算效率，我们开发了一种新的参数估计程序以获取最大似然估计值。进而提出最大化选择似然比检验统计量，用于检验分类时间序列中的突变。通过加拿大不列颠哥伦比亚省圣约翰堡机场上午9时和下午3时记录的日总云量观测数据，对该方法进行了实例验证。