Water Resources Branch, Ontario Ministry of the Environment, 135 St. Clair Ave. W., M4V 1K6, Ontario, Toronto, Canada.
Environ Monit Assess. 1989 Nov;13(2-3):407-28. doi: 10.1007/BF00394242.
Graphical methods can play an important role in the reliable assessment of trends in typically ill behaved river quality data series both as diagnostic tools and as visual corroborative evidence when assumptions required for formal statistical tests are not met. Robust, graphically-oriented trend diagnosis procedures are presented for data series characterized by nonnormal populations, uneven time spacing, nonmonotonic trend and other factors which can create serious problems for standard parametric time series methods. Cleveland's robust locally weighted regression (RLWR) developed for investigating nonlinearity in x-y scatterplots is adapted as a robust/resistant smoothing filter for the analysis of irregular time series comprising quantitative observations. Low powered RLWR trend lines reveal temporally local phenomena, e.g. abrupt jumps (often associated with point source impacts) and periodicities, while higher powered RLWR yields smooth lines characterizing medium and longer term trends. Simple variants of Tukey smoothing concepts are developed for series with censored observations. Applications to Ontario river quality series reveal that graphical evidence is frequently sufficient to obviate the need for formal trend testing. The methods are generally applicable to most time series.
图形方法在可靠评估通常表现不佳的河流质量数据序列的趋势方面可以发挥重要作用，无论是作为诊断工具，还是在不符合正式统计检验所需假设时作为视觉佐证。本文提出了稳健的、面向图形的趋势诊断程序，适用于具有非正态总体、不均匀时间间隔、非单调趋势和其他因素的数据序列，这些因素可能会给标准参数时间序列方法带来严重问题。克利夫兰的稳健局部加权回归（RLWR）最初是为了研究 x-y 散点图中的非线性而开发的，现在被改编为一种稳健/抗扰平滑滤波器，用于分析由定量观测组成的不规则时间序列。低功率 RLWR 趋势线揭示了时间上的局部现象，例如突然的跳跃（通常与点源影响有关）和周期性，而高功率 RLWR 则产生平滑的线，表征中短期趋势。针对有删失观测的序列，开发了图基平滑概念的简单变体。对安大略省河流质量序列的应用表明，图形证据通常足以避免对正式趋势检验的需求。这些方法通常适用于大多数时间序列。
