
Matrix factorization for multivariate time series analysis
Matrix factorization is a powerful data analysis tool. It has been used ...
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Particularities and commonalities of singular spectrum analysis as a method of time series analysis and signal processing
Singular spectrum analysis (SSA), starting from the second half of XX ce...
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HighDimensional Multivariate Forecasting with LowRank Gaussian Copula Processes
Predicting the dependencies between observations from multiple time seri...
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Compact representation of temporal processes in echosounder time series via matrix decomposition
Echosounders are highfrequency sonar systems widely used to observe mid...
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Classification with the matrixvariatet distribution
Matrixvariate distributions can intuitively model the dependence struct...
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Contrastive Multivariate Singular Spectrum Analysis
We introduce Contrastive Multivariate Singular Spectrum Analysis, a nove...
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Low Rank Forecasting
We consider the problem of forecasting multiple values of the future of ...
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On Multivariate Singular Spectrum Analysis
We analyze a variant of multivariate singular spectrum analysis (mSSA), a widely used multivariate time series method, which we find to perform competitively with respect to the stateofart neural network time series methods (LSTM, DeepAR). Its restriction for single time series, singular spectrum analysis (SSA), has been analyzed recently. Despite its popularity, theoretical understanding of mSSA is absent. Towards this, we introduce a natural spatiotemporal factor model to analyze mSSA. We establish the insample prediction error for imputation and forecasting under mSSA scales as 1/√(NT), for N time series with T observations per time series. In contrast, for SSA the error scales as 1/√(T) and for matrix factorization based time series methods, the error scales as 1/min(N, T). We utilize an online learning framework to analyze the onestepahead prediction error of mSSA and establish it has a regret of 1/(√(N)T^0.04) with respect to insample forecasting error. By applying mSSA on the square of the time series observations, we furnish an algorithm to estimate the timevarying variance of a time series and establish it has insample imputation / forecasting error scaling as 1/√(NT). To establish our results, we make three technical contributions. First, we establish that the "stacked" Page Matrix time series representation, the core data structure in mSSA, has an approximate lowrank structure for a large class of time series models used in practice under the spatiotemporal factor model. Second, we extend the theory of online convex optimization to address the variant when the constraints are timevarying. Third, we extend the analysis prediction error analysis of Principle Component Regression beyond recent work to when the covariate matrix is approximately lowrank.
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