Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

Barton, Elena; Al-Sarray, Basad; Chrétien, Stéphane; Jagan, Kavya

doi:10.3390/math6070124

Cited by 3 publications

(3 citation statements)

References 43 publications

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“…The calendar effect is the effect of working days and movable holidays. The working day effect is understood as the effect of a different number of working days in individual periods (months, quarters) on the observed phenomenon (Barton, Al.-Sarray, Chretien, and Jagan, 2018). Business activity of economic operators is more intense on working days than on public holidays (Olejarz-Wahba and Rutkowska-Ziarko, 2015).…”

Section: Methodsmentioning

confidence: 99%

The Level of Economic Development and the Savings Rate of Households

Grzywińska‐Rąpca¹,

Aleksandra²

2021

ERSJ

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Purpose: The aim of this article was to present the G7 household savings rate models, including the extraction and identification of time series components that determine the formation of the studied phenomenon. Design/Methodology/Approach: The research was carried by a detailed analysis of the savings rates of G7 households in individual quarters in the years 2000-2018. Time series decomposition and identification of time series components, including the seasonal component, trend and outliers were made using econometric tools. The analyses used the automatic seasonal adjustment procedures TRAMO-SEATS and ARIMA-X-12. The obtained models were formally verified empirically. Findings: The decomposition of the time series of the G7 household savings rate provided information on the shaping of the analysed phenomenon. Using the Tramo-Seats procedure, it was shown that the savings rate of the United States, Canada and France is not subject to seasonal fluctuations, and the visible fluctuations are the result of the moving average process and outliers. Seasonal savings occurred in the case of Japan, Germany, Italy, and Great Britain. This seasonality was of a different nature, with the largest seasonal deviations recorded for Germany and Italy. Practical implications: In this paper the components of the time series of savings rates of G7 households were analysed and distinguished, showing differences in the development of the analysed phenomenon in individual countries, providing the appropriate economic justification for the differences. Originality/Value: In macroeconomic scale, households play an important role in the economy, creating the conditions for the sustainable development of the economy. They are an important source of financing for business investment and budget deficits. In a microeconomic perspective, a low savings rate can reduce the living conditions of the population, which has many negative effects. Taking this into account the above, learning about the development of the phenomenon under study, which is the household savings rate, allows to predict and adjust economic programs to optimize the desired effects.

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Section: Methodsmentioning

confidence: 99%

The Level of Economic Development and the Savings Rate of Households

Grzywińska‐Rąpca¹,

Aleksandra²

2021

ERSJ

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“…This denoising problem is of crucial importance in many applications and is also known as super-resolution in the literature; see [16,[29][30][31][32][33]. The main motivation behind Cadzow's algorithm is that many signals of interest have low rank Hankelization.…”

Section: A Uniformly Convex Version Of Cadzow's Methodsmentioning

confidence: 99%

Projection Methods for Uniformly Convex Expandable Sets

Chrétien

Bondon

2020

Mathematics

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Many problems in medical image reconstruction and machine learning can be formulated as nonconvex set theoretic feasibility problems. Among efficient methods that can be put to work in practice, successive projection algorithms have received a lot of attention in the case of convex constraint sets. In the present work, we provide a theoretical study of a general projection method in the case where the constraint sets are nonconvex and satisfy some other structural properties. We apply our algorithm to image recovery in magnetic resonance imaging (MRI) and to a signal denoising in the spirit of Cadzow’s method.

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“…The SSA method functions as a mean of decomposing the initial components to three components, i.e. noise, seasonal and trend [9]. This method comprises two corresponding stages that are known as reconstruction and decomposition stages.…”

Section: B Algorithm For Ssamentioning

confidence: 99%

Performance Analysis and Validation of Modified Singular Spectrum Analysis based on Simulation Torrential Rainfall Data

Shaharudin

Ahmad

Mohamed

et al. 2020

Int. J. Adv. Sci. Eng. Inf. Technol.

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A popular method for time series analysis to extract the components of noise and trend from the time series data is called the singular spectrum analysis (SSA). However, the drawback of SSA is its problem in determining the appropriate window length, L for certain data set in confirming patent separation of the components of trend and noise. Another issue that crops up when using SSA is that, over time, the sum of day-today rainfall becomes nearly comparable. In this case, disjoints sets of singular values and distinctive series components could essentially be intermixed, resulting in poor separability between trend and noise components. The introduction of modified SSA is to mitigate the problems efficiently. The performance of modified SSA is measured by using wcorrelation and RMSE based on simulated data. These results show that the parameter L = T/5 was suitable to use in short time series rainfall data. It can be proved by the plot of the extracted trend for modified SSA that appears to conform to the original data configuration for time series rainfall however there is the omission of components of noise predominantly for L = T/5 in detecting the uncharacteristically heavy downpour which could potentially initiate the occurrence of torrential rainfall. In addition, the result shows that average RMSE for reconstructed time series components of modified SSA is much smaller than SSA for each L.

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Decomposition of Dynamical Signals into Jumps, Oscillatory Patterns, and Possible Outliers

Cited by 3 publications

References 43 publications

The Level of Economic Development and the Savings Rate of Households

The Level of Economic Development and the Savings Rate of Households

Projection Methods for Uniformly Convex Expandable Sets

Performance Analysis and Validation of Modified Singular Spectrum Analysis based on Simulation Torrential Rainfall Data

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