Singular Spectrum Analysis (SSA) is an increasingly popular time series filtering and forecasting technique. Owing to its widespread applications in a variety of fields, there is a growing interest towards improving its forecasting capabilities. As such, this paper takes into consideration the Recurrent forecasting approach in SSA (SSA-R) and presents a new mechanism for improving the accuracy of forecasts attainable via this method. The proposed Recurrent SSA-R approach is referred to as Weighted SSA-R (W:SSA-R), and we propose using a weighting algorithm for weigthing the coefficients of the Linear Recurrent Relation (LRR). The performance of forecasts from the W:SSA-R approach are compared with forecasts from the established SSA-R approach. We exploit real data and various simulated time series for the comparison, so as to provide the reader with more conclusive findings. Our results confirm that the W:SSA-R approach can provide comparatively more accurate forecasts and is indeed a viable solution for improving forecasts by SSA.

中文翻译：

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奇异谱分析中的加权线性递归预测

奇异谱分析 (SSA) 是一种越来越流行的时间序列过滤和预测技术。由于其在各个领域的广泛应用，人们对提高其预测能力的兴趣日益浓厚。因此，本文考虑了 SSA 中的循环预测方法 (SSA-R)，并提出了一种新机制来提高通过该方法可获得的预测准确性。所提出的循环 SSA-R 方法称为加权 SSA-R (W:SSA-R)，我们建议使用加权算法对线性循环关系 (LRR) 的系数进行加权。将 W:SSA-R 方法的预测性能与已建立的 SSA-R 方法的预测进行比较。我们利用真实数据和各种模拟时间序列进行比较，以便为读者提供更确凿的发现。我们的结果证实，W:SSA-R 方法可以提供相对更准确的预测，并且确实是改进 SSA 预测的可行解决方案。