Download or read book A Frequency Domain Approach for the Estimation of Parameters of Spatio Temporal Stationary Random Processes written by Tata Subba Rao and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio-temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex valued random variables, an approximate likelihood function is constructed. The sampling properties of the estimators are investigated. It is observed that the expectation of these transforms can be considered to be a frequency domain analogue of the classical variogram. We call this measure frequency variogram. The method is applied to simulated data and also to Pacific wind speed data considered earlier by Cressie and Huang (1999). The proposed method does not depend on the distributional assumptions about the process.
Download or read book On the Frequency Variogram and on Frequency Domain Methods for the Analysis of Spatio Temporal Data written by Tata Subba Rao and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we assume the spatio-temporal process to be intrinsically stationary in time and stationary in space. Our objective here is to present an alternative way, based on frequency domain methods, for modelling the data. We consider the discrete Fourier transforms (DFTs) defined for the (intrinsic) time-series data observed at several locations as our data. We use the well-known property that DFTs are asymptotically uncorrelated and distributed as complex Gaussian in deriving many results. Our objective here is to emphasize the usefulness of the DFTs in the analysis of spatio-temporal data. Under the assumption of intrinsic stationarity, we consider the estimation of frequency variogram (FV) and discuss its asymptotic sampling properties. We show that FV introduced earlier is a frequency decomposition of space-time variogram. The DFTs can be computed very fast using fast Fourier transform algorithms. Assuming that the DFTs of the incremental process satisfy a Laplacian model, an analytic expression for the space-time spectral density and an expression for the FV in terms of the spectral density function for the intrinsic stationary process are derived. The estimation of the parameters of the spectral density is also considered. A statistical test for spatial independence of spatio-temporal data is proposed.
Download or read book A New Covariance Function and Spatio Temporal Prediction Kriging for a Stationary Spatio Temporal Random Process written by T. Subba Rao and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a stationary spatio-temporal random process and let be a sample from the process. Our object here is to predict, given the sample, for all at the locations. To obtain the predictors, we define a sequence of discrete Fourier transforms using the observed time series. We consider these discrete Fourier transforms as a sample from the complex valued random variable. Assuming that the discrete Fourier transforms satisfy a complex stochastic partial differential equation of the Laplacian type with a scaling function that is a polynomial in the temporal spectral frequency, we obtain, in a closed form, expressions for the second-order spatio-temporal spectrum and the covariance function. The spectral density function obtained corresponds to a non-separable random process. The optimal predictor of the discrete Fourier transform is in terms of the covariance functions. The estimation of the parameters of the spatio-temporal covariance function is considered and is based on the recently introduced frequency variogram method. The methods given here can be extended to situations where the observations are corrupted by independent white noise. The methods are illustrated with a real data set.
Download or read book Covariance Modeling and Parameter Estimation for Stationary Spatio temporal Gaussian Random Fields written by Benjamin Adam Shaby and published by . This book was released on 2007 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Filtering written by V.N. Fomin and published by Springer. This book was released on 1999-05-31 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers methods for the optimal processing of random fields. In particular, it studies spatio-temporal filtering problems such as the problem of optimal signal detection (Bayes' approach) and estimating angles of arrival of local signals. The exposition of the problem of optimal filtering is presented with the help of insights from probability theory, functional analysis and mathematical physics. An algorithmic form of the net results facilitates computer-aided applications. Audience: This volume will be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, functional analysis and mathematical physics.
Download or read book Estimation and Smoothing of Stationary Spatial Processes Governed by Elliptic Stochastic Partial Differential Equations written by Zeynep Türkân Yücel and published by . This book was released on 1994 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Input Signals for Parameter Estimation written by Ewaryst Rafajłowicz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-07 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.
Download or read book Nonlinear System Identification written by Stephen A. Billings and published by John Wiley & Sons. This book was released on 2013-09-23 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
Download or read book A New Frequency Domain Approach of Testing for Covariance Stationarity and for Periodic Stationarity in Multivariate Linear Processes written by Carsten Jentsch and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In modelling seasonal time series data, periodically (non-)stationary processes have become quite popular over the last years and it is well known that these models may be represented as higher-dimensional stationary models. In this article, it is shown that the spectral density matrix of this higher-dimensional process exhibits a certain structure if and only if the observed process is covariance stationary. By exploiting this relationship, a new L-type test statistic is proposed for testing whether a multivariate periodically stationary linear process is even covariance stationary. Moreover, it is shown that this test may also be used to test for periodic stationarity. The asymptotic normal distribution of the test statistic under the null is derived and the test is shown to have an omnibus property. The article concludes with a simulation study, where the small sample performance of the test procedure is improved by using a suitable bootstrap scheme.
Download or read book A Frequency Domain Test for a Spatial Unit Root Process written by Andres Ramirez Hassan and published by . This book was released on 2014 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stationarity is a common assumption in statistical inference when data come from a random field, but this hypothesis has to be checked. In this paper, we build a frequency domain statistical test to check a unit root for a spatial autoregressive model, and find its asymptotic distribution. Later, we use Monte Carlo simulations to obtain the small sample properties of the proposed statistical test, and we find that the size of the test is good, and the power of the test improves if the spatial autocorrelation coefficient decreases. Additionally, we find that the size of our test is better than other spatial unit root tests when the data generating process is not a spatial autoregressive model. Finally, we propose a methodology to use frequency domain tests in regional data, and we use it to do an application. Specifically, we study data of electricity demand in the Department of Antioquia (Colombia), and find that statistical evidence based on different tests suggests that electricity consumption does not have a spatial unit root; as a consequence, parameter estimates are sensible. Specifically, we find that the price elasticity of electricity demand is -1.150 while the income elasticity is 0.408.
Download or read book A Spectral Domain Test for Stationarity of Spatio Temporal Data written by Soutir Bandyopadhyay and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many random phenomena in the environmental and geophysical sciences are functions of both space and time; these are usually called spatio-temporal processes. Typically, the spatio-temporal process is observed over discrete equidistant time and at irregularly spaced locations in space. One important aim is to develop statistical models based on what is observed. While doing so a commonly used assumption is that the underlying spatio-temporal process is stationary. If this assumption does not hold, then either the mean or the covariance function is misspecified. This can, for example, lead to inaccurate predictions. In this article we propose a test for spatio-temporal stationarity. The test is based on the dichotomy that Fourier transforms of stochastic processes are near uncorrelated if the process is second-order stationary but correlated if the process is second-order nonstationary. Using this as motivation, a discrete Fourier transform for spatio-temporal data over discrete equidistant times but on irregularly spaced spatial locations is defined. Two statistics which measure the degree of correlation in the discrete Fourier transforms are proposed. These statistics are used to test for spatio-temporal stationarity. It is shown that the same statistics can also be adapted to test for the one-way stationarity (either spatial or temporal stationarity). The proposed methodology is illustrated with a small simulation study.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spatio Temporal Methods in Environmental Epidemiology written by Gavin Shaddick and published by CRC Press. This book was released on 2015-06-17 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological StudiesSpatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and
Download or read book The Application of Higher Order Statistics to Non linear Model Identification and Parameter Estimation in the Time and Frequency Domains written by David Guy and published by . This book was released on 1992 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Digital Signal Processing Handbook written by VIJAY MADISETTI and published by CRC Press. This book was released on 1997-12-29 with total page 1792 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of digital signal processing (DSP) has spurred developments from basic theory of discrete-time signals and processing tools to diverse applications in telecommunications, speech and acoustics, radar, and video. This volume provides an accessible reference, offering theoretical and practical information to the audience of DSP users. This immense compilation outlines both introductory and specialized aspects of information-bearing signals in digital form, creating a resource relevant to the expanding needs of the engineering community. It also explores the use of computers and special-purpose digital hardware in extracting information or transforming signals in advantageous ways. Impacted areas presented include: Telecommunications Computer engineering Acoustics Seismic data analysis DSP software and hardware Image and video processing Remote sensing Multimedia applications Medical technology Radar and sonar applications This authoritative collaboration, written by the foremost researchers and practitioners in their fields, comprehensively presents the range of DSP: from theory to application, from algorithms to hardware.
Download or read book A Collection of Technical Papers written by and published by . This book was released on 1987 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Methods for Spatio Temporal Systems written by Barbel Finkenstadt and published by CRC Press. This book was released on 2006-10-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts w
