Functional singular spectrum analysis

Haghbin, Hossein; Najibi, Seyed Morteza; Mahmoudvand, Rahim; Trinka, Jordan; Maadooliat, Mehdi

doi:10.1002/sta4.330

Cited by 10 publications

(20 citation statements)

References 30 publications

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“…The grouping step is the procedure of rearranging and partitioning the elementary operators X i 's in (20). To do this, we mimic the approaches used in step 3 of Section 2 for the univariate SSA and implement the equivalent functional version of those in Haghbin and Najibi (2019). Note that, in practice, we use a finite set of elementary operators, and one can consider a partition {I 1 , I 2 , .…”

Section: Fssa Algorithmmentioning

confidence: 99%

“…Furthermore, in the diagonal averaging step, we can incorporate the averaging over the associate basis coefficients of x q l,k in ( 22) to obtain the respective basis coefficients for xq i,j . For more details see Haghbin and Najibi (2019).…”

Section: Implementation Strategymentioning

confidence: 99%

“…In this section, first, we present a simulation study to elaborate the use of the FSSA compared with FPCA and MSSA under different scenarios. To do so, we utilize the implementation of the proposed model that is available as an R package named Rfssa in the CRAN repository (Haghbin and Najibi, 2019). We also use the fda (Ramsay et al, 2018) and Rssa (Golyandina et al, 2015) packages to obtain the FPCA and MSSA results.…”

Section: Numerical Studymentioning

confidence: 99%

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Functional Singular Spectrum Analysis

Haghbin¹,

Najibi²,

Mahmoudvand³

et al. 2019

Preprint

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In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate SSA. We explore the advantages of the functional SSA in terms of simulation results and with an application to a call center data. We compare the proposed approach with Multivariate SSA (MSSA) and Functional Principal Component Analysis (FPCA). The results suggest that further improvement to MSSA is possible and the new method provides an attractive alternative to the novel extensions of the FPCA for correlated functions. We have also developed an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.

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Section: Fssa Algorithmmentioning

confidence: 99%

Section: Implementation Strategymentioning

confidence: 99%

Section: Numerical Studymentioning

confidence: 99%

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Functional Singular Spectrum Analysis

Haghbin¹,

Najibi²,

Mahmoudvand³

et al. 2019

Preprint

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“…The main task in SSA is to extract the underlying signals of a time series like the trend, cycle, seasonal and irregular components. It has been applied to a wide range of time series problems, besides signal processing [2], like forecasting [3], missing value imputation [4] or functional time series [5] among others. SSA builds a trajectory matrix by putting together lagged pieces of the original time series and works with the Singular Value Decomposition of this matrix.…”

Section: Introductionmentioning

confidence: 99%

Circulant Singular Spectrum Analysis: A new automated procedure for signal extraction

Bógalo,

Poncela,

Senra

2020

Preprint

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Sometimes, it is of interest to single out the fluctuations associated to a given frequency. We propose a new variant of SSA, Circulant SSA (CiSSA), that allows to extract the signal associated to any frequency specified beforehand. This is a novelty when compared with other procedures that need to identify ex-post the frequencies associated to extracted signals. We prove that CiSSA is asymptotically equivalent to these alternative procedures although with the advantage of avoiding the need of the subsequent frequency identification. We check its good performance and compare it to alternative SSA methods through several simulations for linear and nonlinear time series. We also prove its validity in the nonstationary case. To show how it works with real data, we apply CiSSA to extract the business cycle and deseasonalize the Industrial Production Index of six countries. Economists follow this indicator in order to assess the state of the economy in real time. We find that the estimated cycles match the dated recessions from the OECD showing its reliability for business cycle analysis. Finally, we analyze the strong separability of the estimated components. In particular, we check that the deseasonalized time series do not show any evidence of residual seasonality.

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“…Методи (SSA або Singular Spectrum Analysis або «гусениця» [3,4], Adaptive harmonic components detection and forecasting [5,6,7]…”

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Template-Based Model for Short-Term Forecasting of the Number of Transactions in Retail Clothing Stores

Галуза¹,

Kostiuk²,

Nikulchenko³

et al. 2022

SACIT

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Obtaining predictive values of indicators based on historical data represented by time series plays a crucial role in making business decisions in various industries. One of these areas of application is the task of predicting the number of transactions in retail stores in order to optimally plan the working hours of employees and achieve maximum customer satisfaction with the quality of service. The choice of an appropriate time series forecasting model depends on the forecast horizon, as well as the characteristics of the time series, namely trend, seasonality, cyclicality, and irregularity. Traditional time series analysis and forecasting methods are designed to handle a single seasonality in a time series, but in the presence of multiple seasonality, these methods do not work satisfactorily. The use of time series decomposition methods is characterized by computational complexity. The use of machine learning methods is also not always advisable for a number of different reasons. Thus, it is necessary to use simple adaptive models, based on selected patterns, for recurring seasonal data of complex structure. The main goal of this article is to develop a successful adaptive model and propose methods for using it for short-term forecasting of the number of transactions based on time series data. For estimation purposes, a set of hourly time series of the number of customers (transactions) of some retail chain stores, characterized by multiple seasonality, is used. The results of computational experiments show that the proposed template-based model is quite effective for obtaining short-term predictive values. This model, characterized by simplicity, intuitiveness and a minimum number of tuning parameters, can actually be applied to any area of data represented by time series.

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Functional singular spectrum analysis

Cited by 10 publications

References 30 publications

Functional Singular Spectrum Analysis

Functional Singular Spectrum Analysis

Circulant Singular Spectrum Analysis: A new automated procedure for signal extraction

Template-Based Model for Short-Term Forecasting of the Number of Transactions in Retail Clothing Stores

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