Competitive principal component analysis for locally stationary time series

Fancourt, Craig; Prı́ncipe, José C.

doi:10.1109/78.726819

Cited by 17 publications

(7 citation statements)

References 19 publications

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“…For a correlation decomposition, the covariance assigned to each mode of the decomposition is equivalent to the squared eigenvalue, k j 2 . The normalized eigenvalues, k j /Rk, therefore, represent that percentage of the rootmean-square error accounted for by the jth mode (FANCOURT and PRINCIPE 1998;PREISENDORFER 1988;SMITH et al 2007) and are shown in Fig. 5 and tabulated in Tables 3 and 4.…”

Section: Model Errormentioning

confidence: 99%

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Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

Tiampo

Mazzotti

James

2011

Pure Appl. Geophys.

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International audienceContinuous Global Positioning System (CGPS) position time series from eastern North America constrain the pattern and magnitude of regional crustal deformation. Initial analysis delineates consistent uplift patterns, as expected from glacial isostatic adjustment (GIA) predictions, but the associated horizontal deformation is not definitive, in part due to the short time periods for a significant number of the available stations. We employ an eigenpattern decomposition in order to define a unique, finite set of deformation patterns for this continuous GPS data. Similar in nature to the empirical orthogonal functions historically employed in the analysis of atmospheric and oceanographic phenomena, the method derives the eigenvalues and eigenstates from the diagonalization of the correlation matrix using a Karhunen-Loeve expansion (KLE). The KLE technique is used to identify the important modes in both time and space for the CGPS data, modes that potentially include signals such as horizontal and vertical GIA, tectonic strain, and seasonal effects. Here we filter both the vertical and horizontal velocity patterns on different spatiotemporal scales in order to study the potential geophysical sources, after the removal of correlated and random noise. The method is successful in disaggregating the linear vertical signal from more variable and less spatially correlated signals. The vertical and horizontal results are compared to the predictions of the ICE-3G GIA loading model with a number of plausible mantle viscosity profiles. The horizontal velocity analysis allows for qualitative differentiation between several potential GIA models and suggests that, with longer time series, this technique can be employed to remove correlated noise and improve estimates of crustal strain patterns and their sources

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Section: Model Errormentioning

confidence: 99%

“…Consequently, the remaining modes, when summed, must represent the greatest portion of the random noise in the data. We are, therefore, testing to see which modes are significant above that random noise (FANCOURT and PRINCIPE 1998;SMITH et al 2007).…”

Section: Modal Recombinationmentioning

confidence: 99%

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

Tiampo

Mazzotti

James

2011

Pure Appl. Geophys.

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“…The TKM has also been used in object recognition (Lakany & Hayes, 1997) and mobile robot navigation (Lambrinos & Scheier, 1995). The SARDNET (James & Miikkulainen, 1995), the networks by Euliano and Principe (1995) and Fancourt and Principe (1997), and the recurrent SOM (Koskela, Varsta, Heikkonen, & Kaski, 1998) also belong to the class of unsupervised STCNs with FED memories. They have been applied to letter and word sequence detection, segmentation of piecewise time series, and prediction of time series, respectively.…”

Section: Feedforward Exponential Decaymentioning

confidence: 98%

“…This combination of techniques can be understood as a type of temporal PCA. Unfortunately, as pointed out by Fancourt and Principe (1997) such a method is very slow to converge because the principal components must converge approximately in order, from largest to smallest associated eigenvalue.…”

Section: Parameter Update Functionmentioning

confidence: 98%

A Taxonomy for Spatiotemporal Connectionist Networks Revisited: The Unsupervised Case

2003

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Spatiotemporal connectionist networks (STCNs) comprise an important class of neural models that can deal with patterns distributed in both time and space. In this article, we widen the application domain of the taxonomy for supervised STCNs recently proposed by Kremer (2001) to the unsupervised case. This is possible through a reinterpretation of the state vector as a vector of latent (hidden) variables, as proposed by Meinicke (2000). The goal of this generalized taxonomy is then to provide a nonlinear generative framework for describing unsupervised spatiotemporal networks, making it easier to compare and contrast their representational and operational characteristics. Computational properties, representational issues, and learning are also discussed, and a number of references to the relevant source publications are provided. It is argued that the proposed approach is simple and more powerful than the previous attempts from a descriptive and predictive viewpoint. We also discuss the relation of this taxonomy with automata theory and state-space modeling and suggest directions for further work.

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“…Del Negro and Otrok (2008) developed a dynamic factor model with time-varying factor loadings following a random walk and with stochastic volatility in both the latent factors and idiosyncratic components. The situation where breaks occur at random time points has already been covered by Fancourt and Principe (1998) with a model based on piecewise constant loadings. A recent approach of Stock and Watson (2008) investigates the effect of structural instabilities on the forecasting ability of a dynamic factor model with a possible abruptly changing parameter in an autoregressive factor specification.…”

Section: Introductionmentioning

confidence: 99%

Fitting dynamic factor models to non-stationary time series

Eichler

Motta

Sachs

2011

Journal of Econometrics

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a b s t r a c tFactor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni-or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time by proposing a deterministic time variation of its loadings. In this respect we generalize the existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as a time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a ''double-asymptotic'' framework of both cross-section and time dimension tending to infinity. The performance of the estimators is illustrated by a simulation study and an application to a macroeconomic data set.

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Competitive principal component analysis for locally stationary time series

Abstract: Abstract-

Cited by 17 publications

References 19 publications

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

A Taxonomy for Spatiotemporal Connectionist Networks Revisited: The Unsupervised Case

Fitting dynamic factor models to non-stationary time series

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