Time series with strong periodicity and non-stationary character in terms of magnitude and frequency which are changing over measurement period can be decomposed into time-varying trend, seasonal and cyclical components by dynamic harmonic regression (DHR) modeling in the state-space framework. The time-variable parameters of the components are first associated with a generalized random walk process, and then, state parameters are estimated by the recursive Kalman filtering and fixed interval smoothing algorithms. Missed points are filled by the DHR interpolation, and change points are detected by both visual inspection and the Pettitt test. Sea level series at tide gauges, which consist of accelerated trend and strong periodicity, are therefore suitable for DHR modeling. Time-varying trend, seasonal and cyclical components are extracted by the DHR modeling from the monthly mean sea level series longer than 15 years at seven stations within the Arabian Gulf. The DHR model accounts for 90–96% of variation of the monthly series, while the seasonal and cyclical components account for 64–85% and 2–7%, respectively. Average relative sea level rate (RSLR) and absolute sea level rate (ASLR) over the Arabian Gulf are found $$1.67 \pm 0.05$$ 1.67 ± 0.05 mm/year and 1.93 ± 0.05 mm/year, respectively.

中文翻译：

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阿拉伯湾内潮汐仪月平均海平面的动态谐波回归建模

在状态空间框架下，通过动态谐波回归（DHR）建模，可以将随测量周期变化的具有强周期性和幅度和频率非平稳特性的时间序列分解为时变趋势、季节性和周期性分量。组件的时变参数首先与广义随机游走过程相关联，然后通过递归卡尔曼滤波和固定间隔平滑算法估计状态参数。遗漏点由 DHR 插值补齐，变化点由目视检查和 Pettitt 检验检测。潮位计上的海平面序列具有加速趋势和强周期性，因此适用于 DHR 建模。时变趋势，DHR 建模从阿拉伯湾七个站点超过 15 年的月平均海平面序列中提取季节性和周期性分量。DHR 模型占月序列变异的 90-96%，而季节性和周期性分量分别占 64-85% 和 2-7%。阿拉伯湾的平均相对海平面率 (RSLR) 和绝对海平面率 (ASLR) 分别为 $1.67 \pm 0.05$$ 1.67 ± 0.05 毫米/年和 1.93 ± 0.05 毫米/年。