Statistics and Its Interface

Volume 16 (2023)

Number 1

Special issue on recent developments in complex time series analysis – Part I

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Forecasting industrial production indices with a new singular spectrum analysis forecasting algorithm

Pages: 31 – 42



Sofia Borodich Suarez (Department of Economics and Management, University of Luxembourg)

Saeed Heravi (School of Business, Cardiff University, Cardiff, Wales, United Kingdom)

Andrey Pepelyshev (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)


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.


singular spectrum analysis, forecasting, root mean square error

2010 Mathematics Subject Classification


The work of A. Pepelyshev was partially supported by the Russian Foundation for Basic Research (project no. 20-01-00096).

Received 6 May 2021

Accepted 18 July 2021

Published 28 December 2022