Singular spectrum analysis (SSA) is a non-parametric forecasting and filtering method that has many applications in a variety of fields such as signal processing, economics and time series analysis. One of the four steps of the SSA, which is called the grouping step, plays a pivotal role in the SSA because reconstruction and forecasting of results are directly affected by the outputs of this step. Usually, the grouping step of SSA is time consuming as the interpretable components are manually selected. An alternative more optimized approach is to apply automatic grouping methods. In this paper, a new dissimilarity measure between two components of a time series that is based on various matrix norms is first proposed. Then, using the new dissimilarity matrices, the capabilities of different hierarchical clustering linkages are compared to identify appropriate groups in the SSA grouping step. The performance of the proposed approach is assessed using the corrected Rand index as validation criterion and utilizing various real-world and simulated time series.

In all fields of quantitative research, analysing data with missing values is an excruciating challenge. It should be no surprise that given the fragmentary nature of fossil records, the presence of missing values in geographical databases is unavoidable. As in such studies ignoring missing values may result in biased estimations or invalid conclusions, adopting a reliable imputation method should be regarded as an essential consideration. In this study, the performance of singular spectrum analysis (SSA) based on $L_1$ norm was evaluated on the compiled ${\delta }^{13}C$ data from East Africa soil carbonates, which is a world targeted historical geology data set. Results were compared with ten traditionally well-known imputation methods showing $L_1$ -SSA performs well in keeping the variability of the time series and providing estimations which are less affected by extreme values, suggesting the method introduced here deserves further consideration in practice.

The Singular Spectrum Analysis (SSA) technique is a non-parametric powerful method in the field of time series analysis whose popularity has increased in recent years owing to its widespread applications. Recurrent forecasting is one of the important forecasting methods in SSA. In this paper, the forecasting accuracy of recurrent forecasts is improved via the introduction of a new recurrent forecasting algorithm. In the novel approach, the recurrent coefficients are generated from the filtered series which has less noise and thus enables one to achieve the better forecasts. The performance of the new method has been compared with the established recurrent forecasting method. The comparison involves applications to various real and simulated time series. The obtained results confirm that the new approach can provide more accurate forecasts.

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the $L_1$ norm-based version of Singular Spectrum Analysis (SSA), namely $L_1$-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially $L_1$-SSA can provide better imputation in comparison to other methods.

Singular spectrum analysis (SSA) is a popular filtering and forecasting method that is used in a wide range of fields such as time series analysis and signal processing. A commonly used approach to identify the meaningful components of a time series in the grouping step of SSA is the utilization of the visual information of eigentriples. Another supplementary approach is that of employing an algorithm that performs clustering based on the dissimilarity matrix defined by weighted correlation between the components of a time series. The SSA literature search revealed that no investigation has compared the various clustering methods. The aim of this paper was to compare the effectiveness of different hierarchical clustering linkages to identify the appropriate groups in the grouping step of SSA. The comparison was performed based on the corrected Rand (CR) index as a comparison criterion that utilizes various simulated series. It was also demonstrated via two real-world time series how one can proceed, step-by-step, to conduct grouping in SSA using a hierarchical clustering method. This paper is supplemented with accompanying R codes.