A new parsimonious recurrent forecasting model in singular spectrum analysis

Mahmoudvand, Rahim; Rodrigues, Paulo Canas

doi:10.1002/for.2484

Cited by 18 publications

(17 citation statements)

References 12 publications

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“…Figure shows 3 illustrative simulation plots based on the USAccDeaths data, together with the reconstructed values based on the classical and robust versions of the SSA, considering: no contamination (top plot); scenario 1(ii) (2nd plot); scenario 1(iii) (3rd plot); and scenario 2 with

k = \frac{{\overset{Y}{true}}_{N}}{2} = 4394.4

and l = 12 observations contaminated (bottom plot). The model fit was made by considering a window length of 24 and 13 eigentriples for the reconstruction stage, following the suggestion by Mahmoudvand and Rodrigues . When the time series data are uncontaminated, the classical SSA performs slightly better than the robust counterpart, as is usually expected from robust approaches (Figure ; top plot).…”

Section: Simulation Studymentioning

confidence: 89%

A robust approach to singular spectrum analysis

Rodrigues

Lourenço

Mahmoudvand

2018

Quality & Reliability Eng

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Singular spectrum analysis (SSA) is a nonparametric method for time series analysis and forecasting that incorporates elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems, and signal processing. Although this technique has shown to be advantageous over traditional model‐based methods, in particular, one of the steps of the SSA algorithm, which refers to the singular value decomposition (SVD) of the trajectory matrix, is highly sensitive to data contamination. Specifically, and because SVD decomposition is least squares based, the presence of a single outlier, if extreme, may be enough to draw the leading principal component towards itself resulting in possible misinterpretations, which may subsequently, in particular and in the case of time series analysis, lead to reduced quality of model fit and forecast accuracy. In order to alleviate this problem, a robust SSA algorithm is proposed, where a robust SVD procedure replaces the least squares based one in the original SSA procedure. The SSA and the robust SSA approaches are compared in terms of model fit quality via Monte Carlo simulations that contemplate both clean and noisy/contaminated time series. The adequacy and value of the proposed approach is then compared with the standard SSA using real data about the industrial production index.

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k = \frac{{\overset{Y}{true}}_{N}}{2} = 4394.4

Section: Simulation Studymentioning

confidence: 89%

A robust approach to singular spectrum analysis

Rodrigues

Lourenço

Mahmoudvand

2018

Quality & Reliability Eng

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“…Further explanation and intuition about this measure can be found in [ 5 , 28 ]. Other proposals for this choice were proposed by, e.g., [ 30 , 31 ].…”

Section: Methodsmentioning

confidence: 99%

“…The standard recurrent SSA forecasting algorithm assumes that a given observation can be written as a linear combination of the

previous observations [ 5 , 6 , 30 ]. The coefficients of those linear combinations in the classical SSA forecasting algorithm are obtained based on the left singular vectors, U , of the trajectory matrix

.…”

Section: Methodsmentioning

confidence: 99%

The Decomposition and Forecasting of Mutual Investment Funds Using Singular Spectrum Analysis

Rodrigues

Pimentel

Messala

et al. 2020

Entropy

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Singular spectrum analysis (SSA) is a non-parametric method that breaks down a time series into a set of components that can be interpreted and grouped as trend, periodicity, and noise, emphasizing the separability of the underlying components and separate periodicities that occur at different time scales. The original time series can be recovered by summing all components. However, only the components associated to the signal should be considered for the reconstruction of the noise-free time series and to conduct forecasts. When the time series data has the presence of outliers, SSA and other classic parametric and non-parametric methods might result in misleading conclusions and robust methodologies should be used. In this paper we consider the use of two robust SSA algorithms for model fit and one for model forecasting. The classic SSA model, the robust SSA alternatives, and the autoregressive integrated moving average (ARIMA) model are compared in terms of computational time and accuracy for model fit and model forecast, using a simulation example and time series data from the quotas and returns of six mutual investment funds. When outliers are present in the data, the simulation study shows that the robust SSA algorithms outperform the classical ARIMA and SSA models.

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“…The introduction of the nonparametric time series analysis and forecasting technique of singular spectrum analysis (SSA) is closely associated with the work of Broomhead and King (, ). Since then, SSA has progressed rapidly and transformed itself into a powerful technique that is increasingly exploited for providing solutions to real‐world problems in a variety of different fields; see, for example, Gong, Song, He, Gong, and Ren (), Merte (), Yu, Li, and Zhang (), Mahmoudvand and Rodrigues (), Khan and Poskitt (), Hassani, Ghodsi, Silva, and Heravi (), Hassani, Silva, Antonakakis, Filis, and Gupta (), Hassani, Webster, Silva, and Heravi (), Lai and Guo (), Ghodsi, Silva, and Hassani (), and Silva and Hassani (). Few reasons underlying this augmented usage of SSA can be partly attributed to its nonparametric nature.…”

Section: Introductionmentioning

confidence: 99%

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

Silva

Hassani

Heravi

2018

Journal of Forecasting

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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 is 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 the cases. Accordingly, this new approach succeeds in identifying leading indicators and is a viable option for selecting the SSA choices L and r which minimises a loss function.

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A new parsimonious recurrent forecasting model in singular spectrum analysis

Cited by 18 publications

References 12 publications

A robust approach to singular spectrum analysis

A robust approach to singular spectrum analysis

The Decomposition and Forecasting of Mutual Investment Funds Using Singular Spectrum Analysis

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

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