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.

scholarly journals Some asymptotic results for the periodogram of a stationary time series

1965 ◽  
Vol 5 (1) ◽  
pp. 107-128 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Spectral Density ◽  
Spectral Distribution ◽  
Angular Frequency ◽  
Stationary Time Series ◽  
Asymptotic Results ◽  
Stationary Time ◽  
Spectral Distribution Function

Let x1, x2,…, xn, be n consecutive observations generated by a stationary time series {x}, t = 0, ±1, ±2,…, with E(xt2) < ∈. The periodogram of the set of observations, which may be defined as a function In of angular frequency with range [0, π] that is proportional to , plays an important part in methods of making inferences about the structure of {xt}, particularly its spectral distribution function or spectral density.

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 Estimating common trends in multivariate time series using dynamic factor analysis

2003 ◽  
Vol 14 (7) ◽  
pp. 665-685 ◽  
Author(s):  
A. F. Zuur ◽  
R. J. Fryer ◽  
I. T. Jolliffe ◽  
R. Dekker ◽  
J. J. Beukema
Keyword(s):  
Time Series ◽  
Factor Analysis ◽  
Multivariate Time Series ◽  
Dynamic Factor Analysis ◽  
Dynamic Factor ◽  
Common Trends

Dynamic factor analysis of nonstationary multivariate time series

Psychometrika ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 333-349 ◽  
Author(s):  
Peter C. M. Molenaar ◽  
Jan G. De Gooijer ◽  
Bernhard Schmitz
Keyword(s):  
Time Series ◽  
Factor Analysis ◽  
Multivariate Time Series ◽  
Dynamic Factor Analysis ◽  
Dynamic Factor

scholarly journals Estimation and classification of temporal trends to support integrated ecosystem assessment

2020 ◽  
Author(s):  
Hiroko Kato Solvang ◽  
Benjamin Planque
Keyword(s):  
Time Series ◽  
Barents Sea ◽  
Multivariate Time Series ◽  
Marine Ecosystem ◽  
Temporal Trends ◽  
Dynamic Factor ◽  
Short Time Series ◽  
Common Trends ◽  
Common Trend ◽  
Short Time

Abstract We propose a trend estimation and classification (TREC) approach to estimating dominant common trends among multivariate time series observations. Our methods are based on two statistical procedures that includes trend modelling and discriminant analysis for classifying similar trend (common trend) classes. We use simulations to evaluate the proposed approach and compare it with a relevant dynamic factor analysis in the time domain, which was recently proposed to estimate common trends in fisheries time series. We apply the TREC approach to the multivariate short time series datasets investigated by the ICES integrated assessment working groups for the Norwegian Sea and the Barents Sea. The proposed approach is robust for application to short time series, and it directly identifies and classifies the dominant trends underlying observations. Based on the classified trend classes, we suggest that communication among stakeholders like marine managers, industry representatives, non-governmental organizations, and governmental agencies can be enhanced by finding the common tendency between a biological community in a marine ecosystem and the environmental factors, as well as by the icons produced by generalizing common trend patterns.

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