scholarly journals A wavelet-based approach for imputation in nonstationary multivariate time series

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Rebecca E. Wilson ◽  
Idris A. Eckley ◽  
Matthew A. Nunes ◽  
Timothy Park
Keyword(s):  
Time Series ◽  
Health Monitoring ◽  
Multivariate Time Series ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Data Imputation ◽  
Missing Observations ◽  
Novel Method ◽  
Monitoring Application ◽  
Successful Analysis

AbstractMany multivariate time series observed in practice are second order nonstationary, i.e. their covariance properties vary over time. In addition, missing observations in such data are encountered in many applications of interest, due to recording failures or sensor dropout, hindering successful analysis. This article introduces a novel method for data imputation in multivariate nonstationary time series, based on the so-called locally stationary wavelet modelling paradigm. Our methodology is shown to perform well across a range of simulation scenarios, with a variety of missingness structures, as well as being competitive in the stationary time series setting. We also demonstrate our technique on data arising in a health monitoring application.

scholarly journals Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property

2021 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Alexander Kushnir ◽  
Alexander Varypaev
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Multivariate Time Series ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Stationary Time Series ◽  
Strong Mixing ◽  
Statistical Estimates ◽  
Distribution Parameters ◽  
M Estimates

The publication is devoted to studying asymptotic properties of statistical estimates of the distribution parameters u∈Rq of a multidimensional random stationary time series zt∈Rm, t∈ℤ satisfying the strong mixing conditions. We consider estimates u^nδ(z¯n), z¯n=(z1T,…,znT)T∈Rmn that provide in asymptotic n→∞ the maximum values for some objective functions Qn(z¯n;u), which have properties similar to the well-known property of local asymptotic normality. These estimates are constructed by solving the equations δn(z¯n;u)=0, where δn(z¯n;u) are arbitrary functions for which δn(z¯n;u)−gradhQn(z¯n;u+n−1/2h)→0(n→∞) in Pn,u(z¯n)-probability uniformly on u∈U, were U is compact in Rq. In many cases, the estimates u^nδ(z¯n) have the same asymptotic properties as well-known M-estimates defined by equations u^nQ(z¯n)=arg maxu∈UQn(z¯n;u) but often can be much simpler computationally. We consider an algorithmic method for constructing estimates u^nδ(z¯n), which is similar to the accumulation method first proposed by R. Fischer and rigorously developed by L. Le Cam. The main theoretical result of the article is the proof of the theorem, in which conditions of the asymptotic normality of estimates u^nδ(z¯n) are formulated, and the expression is proposed for their matrix of asymptotic mean-square deviations limn→∞nEn,u{(u^δ(z¯n)−u)(u^δ(z¯n)−u)T}.

scholarly journals On Independent Component Analysis with Stochastic Volatility Models

2017 ◽  
Vol 46 (3-4) ◽  
pp. 57-66 ◽  
Author(s):  
Markus Matilainen ◽  
Jari Miettinen ◽  
Klaus Nordhausen ◽  
Hannu Oja ◽  
Sara Taskinen
Keyword(s):  
Time Series ◽  
Independent Component Analysis ◽  
Stochastic Volatility ◽  
Financial Time Series ◽  
Multivariate Time Series ◽  
Component Analysis ◽  
Independent Component ◽  
Stationary Time Series ◽  
Volatility Models ◽  
High Volatility

Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to capture nonlinear autocorrelation of the time series and extract the independent components. Simulation study shows that the proposed method outperforms the existing methods when latent components follow GARCH and SV models. This paper is an invited extended version of the paper presented at the CDAM 2016 conference.

ASYMPTOTIC THEORY FOR SPECTRAL DENSITY ESTIMATES OF GENERAL MULTIVARIATE TIME SERIES

2017 ◽  
Vol 34 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Wei Biao Wu ◽  
Paolo Zaffaroni
Keyword(s):  
Time Series ◽  
Spectral Density ◽  
Multivariate Time Series ◽  
Rates Of Convergence ◽  
Stationary Time Series ◽  
Regularity Conditions ◽  
Dynamic Factor ◽  
Asymptotic Results ◽  
Density Estimates ◽  
Convergence Results

We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.

A cointegration approach for cable anomaly warning based on structural health monitoring data: An application to cable-stayed bridges

2020 ◽  
Vol 23 (13) ◽  
pp. 2789-2802
Author(s):  
Zi-Yuan Fan ◽  
Qiao Huang ◽  
Yuan Ren ◽  
Zhi-Yuan Zhu ◽  
Xiang Xu
Keyword(s):  
Time Series ◽  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Environmental Temperature ◽  
Warning System ◽  
Stationary Time Series ◽  
Structural Health ◽  
Residual Series ◽  
Cable Forces ◽  
Cable Stayed Bridges

For long-span cable-stayed bridges, cables are one of the most important components to resist various actions. With the application of structural health monitoring technique, real-time recording of cable forces is achieved, and hence, the warning system on cable anomaly established. However, it is still difficult and there are challenges to conduct the warning system effectively, especially due to the phenomena of false alarm or omission. A practical reason is the warning index’s sensitivity to the ambient environment. Temperature variations, for instance, usually disturb the force-based cable anomaly warning and result in the false evaluation of structural condition. In view of eliminating the effects of environmental temperature, cointegration, a statistical concept from econometrics, is employed in cable anomaly warning studies. An approach that extracts warning index by linear combination of two non-stationary time series using the cointegration algorithm is developed in order to produce a more stationary cointegrated residual series (warning index series). The calculated stationary relationship between two time series is insensitive to the influence of environmental temperature and is capable of cable anomaly warning. Specifically, the framework of the cable anomaly warning system is first proposed. Subsequently, time-series test methods are introduced to check the non-stationary order and calculate the cointegration parameters of measured cable forces and environmental temperature. The computed cointegrated residual series is fed into statistical analysis as a warning index and the procedure of cable anomaly warning under the influence of environmental temperature is illustrated in detail. Finally, a case study for a cable-stayed bridge is demonstrated with results and discussions.

Point-Wise Dimension Estimate of Nonstationary, Multi-Episode, Time-Series and Application to Gearbox Signal

1999 ◽  
Author(s):  
D. C. Lin ◽  
B. J. Augustine ◽  
M. F. Golnaraghi
Keyword(s):  
Time Series ◽  
First Passage Time ◽  
Passage Time ◽  
Nonstationary Time Series ◽  
Stationary Time Series ◽  
Dimension Estimate ◽  
Estimation Algorithms ◽  
Data Segment ◽  
Multiple Episode ◽  
Autocorrelation Time

Abstract Dimensions of nonstationary time series is studied. The nonstationarity is considered to be due to multiple episode where an episode is a piece of stationary time series. The dimension estimation algorithms in the literature can be naturally extended to study multi-episode time series by restricting the calculation on data segment of pre-determined length. Inevitably, more than one episode will be included in the segment. This work focuses on finding when such dimension estimate has a local interpretation as the dimension of the episode. It was found that the local interpretation is valid if there is a large enough difference in the autocorrelation time of the episodes. This is termed EES. In practice, the average first passage time of the reconstructed “orbit” can be used to determine EES. Numerical evidence of these results are given and the application to the mechanical gearbox signal are shown.

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