A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact asymptotic distribution of the changepoint existence test statistic gauging whether or not a second segment is necessary. The identified asymptotic distribution, a supremum of a Gaussian process over the unit interval, is rather unwieldy. The work presented here provides the result and its derivation; quantiles of the asymptotic distribution are presented for the user. This addresses a subtle gap in the changepoint literature.

翻译：单一连接点变点模型将时间序列划分为两个区段，通过在变点时间处约束估计的分段线性回归响应保持连续性而连接。本文推导了检验变点存在性的检验统计量的精确渐近分布，该统计量用于判断是否需要第二个区段。所识别的渐近分布——单位区间上高斯过程的上确界——相当复杂。本文提供了该结果及其推导过程，并给出了渐近分布的分位数以供使用者参考。这填补了变点文献中一个细微的空白。