Univariate Singular Spectrum Analysis Research Articles

Modeling and forecasting of principal minerals production

Although coal reserves are abundant in Pakistan, still share of gas and oil is about 65% in the energy mix. Pakistan, despite being a mineral-enriched country, is facing an alarming situation as its power generation is based on foreign exchange. The mineral sector of Pakistan is dominated by four principal minerals which are gas, oil, gypsum, and coal, while gypsum being a source of reclamation and poverty reduction. There is a strong need to analyze and forecast the production of these four principal minerals to cope up with emerging challenges. Data contains 114 observations from the period of July 2005 to December 2014, measured in terms of metric tonnes (MT). In parametric models, Box-Jenkins (B-J) methodology, a regression model with auto-regressive errors (ARAR), and Holt-Winter (HW) method are used to model. In nonparametric models, univariate singular spectrum analysis (SSA) and multivariate SSA (MSSA) modeling approach are applied. Data is split into train and test data in order to specify a suitable model for forecasting. Root Mean Square Error (RMSE), Mean Absolute Percentage Error, and Theil’s U statistic are utilized as the measure of accuracy. For gas and coal, HW model is a suitable model to forecast. For gypsum and oil, Auto-regressive Integrated Moving Average (Box Jenkins ARIMA) and MSSA provide more accurate predictions, respectively. The forecasts for gas and gypsum as compared to 2014 are expected to be approximately 11 % and 45 %, respectively, more in 2020. In 2020, the forecasts of oil are expected to be eight times more than in 2014. The production of coal in 2020 is expected to decrease 12 % than in 2014. There is a strong need to optimize the production of coal by providing incentives for exploration and mining. The stakeholders should make serious efforts to bring the production of coal at an optimum level such as by providing modern equipment and high incentives to promote coal mining and exploration.

Functional singular spectrum analysis

In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is illustrated by an interesting example of remote sensing data. Also, we develop an efficient and user‐friendly R package and a shiny web application to allow interactive exploration of the results.

Modeling European industrial production with multivariate singular spectrum analysis: A cross‐industry analysis

In this paper, an optimized multivariate singular spectrum analysis (MSSA) approach is proposed to find leading indicators of cross‐industry relations between 24 monthly, seasonally unadjusted industrial production (IP) series for German, French, and UK economies. Both recurrent and vector forecasting algorithms of horizontal MSSA (HMSSA) are considered. The results from the proposed multivariate approach are compared with those obtained via the optimized univariate singular spectrum analysis (SSA) forecasting algorithm to determine the statistical significance of each outcome. The data are rigorously tested for normality, seasonal unit root hypothesis, and structural breaks. The results are presented such that users can not only identify the most appropriate model based on the aim of the analysis, but also easily identify the leading indicators for each IP variable in each country. Our findings show that, for all three countries, forecasts from the proposed MSSA algorithm outperform the optimized SSA algorithm in over 70% of cases. Accordingly, this new approach succeeds in identifying leading indicators and is a viable option for selecting the SSA choices L and r, which minimizes a loss function.

Forecasting mortality rate by multivariate singular spectrum analysis

In this paper, we investigate the possibility of using multivariate singular spectrum analysis (SSA), a nonparametric technique in the field of time series analysis, for mortality forecasting. We consider a real data application with 9 European countries: Belgium, Denmark, Finland, France, Italy, Netherlands, Norway, Sweden, and Switzerland, over a period 1900 to 2009, and a simulation study based on the data set. The results show the superiority of multivariate SSA in comparison with the univariate SSA, in terms of forecasting accuracy.

A Hybrid Short-Term Power Load Forecasting Model Based on the Singular Spectrum Analysis and Autoregressive Model

Short-term power load forecasting is one of the most important issues in the economic and reliable operation of electricity power system. Taking the characteristics of randomness, tendency, and periodicity of short-term power load into account, a new method (SSA-AR model) which combines the univariate singular spectrum analysis and autoregressive model is proposed. Firstly, the singular spectrum analysis (SSA) is employed to decompose and reconstruct the original power load series. Secondly, the autoregressive (AR) model is used to forecast based on the reconstructed power load series. The employed data is the hourly power load series of the Mid-Atlantic region in PJM electricity market. Empirical analysis result shows that, compared with the single autoregressive model (AR), SSA-based linear recurrent method (SSA-LRF), and BPNN (backpropagation neural network) model, the proposed SSA-AR method has a better performance in terms of short-term power load forecasting.