Existing time series analysis and forecasting approaches struggle to produce accurate results in application to time series with complex trend, such as those commonly displayed by indices of industrial production (IIPs). In this study, a new version of the Singular Spectrum Analysis (SSA) technique is developed, namely the Separate Trend and Seasonality (SSA‑STS) forecasting algorithm. Its performance is compared to those of benchmark, classical times series forecasting methods, including Basic SSA (the core version of SSA), ARIMA, Exponential Smoothing (ETS) and Neural Network (NN). The methods in this study are applied to both simulated and real data. The latter includes twenty four monthly series of seasonally unadjusted IIPs of various sectors for the UK, Germany and France. Using the out-of-sample forecasts, the results of this newly developed SSA‑STS algorithm were compared to the other aforementioned forecasting schemes by the means of pooled Root-Mean-Square-Error (RMSE). The pooling is done based on the number of steps ahead the forecasts extend, allowing for the performance of the methods to be evaluated on short and long horizons. The Kolmogorov–Smirnov Predictive Accuracy (KSPA) statistical test is applied to certify whether the errors produced by SSA‑STS are statistically significantly smaller than those of all the benchmark methods. Since this new technique is based on separate trend and seasonality forecasting, it overcomes the difficulties in forecasting series with complex trends and seasonality, thus demonstrating a clear advantage over other methods in such particular cases.

中文翻译：

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用新的奇异谱分析预测算法预测工业生产指数

现有的时间序列分析和预测方法难以在应用于具有复杂趋势的时间序列时产生准确的结果，例如工业生产指数 (IIP) 通常显示的那些。在这项研究中，开发了一种新版本的奇异谱分析（SSA）技术，即分离趋势和季节性（SSA-STS）预测算法。其性能与基准、经典时间序列预测方法的性能进行了比较，包括基本 SSA（SSA 的核心版本）、ARIMA、指数平滑 (ETS) 和神经网络 (NN)。本研究中的方法适用于模拟数据和真实数据。后者包括英国、德国和法国各行业的 24 个月度系列未经季节性调整的国际投资头寸。使用样本外预测，这种新开发的 SSA-STS 算法的结果通过池均方根误差 (RMSE) 与上述其他预测方案进行了比较。池化是根据预测扩展的提前步数完成的，允许在短期和长期范围内评估方法的性能。Kolmogorov-Smirnov Predictive Accuracy (KSPA) 统计测试用于验证 SSA-STS 产生的误差在统计上是否显着小于所有基准方法的误差。由于这种新技术基于单独的趋势和季节性预测，它克服了预测具有复杂趋势和季节性的序列的困难，因此在这种特殊情况下比其他方法具有明显的优势。