Author: Robert KohnPublisher:
ISBN:
Category :
Languages : en
Pages : 10
Book Description
Fixed Interval Estimation in State Space Models when Some of the Data are Missing Or Aggregated 1/2
Author: Robert KohnForecasting, Structural Time Series Models and the Kalman Filter
Author: Andrew C. HarveyPublisher: Cambridge University Press
ISBN: 1107717140
Category : Business & Economics
Languages : en
Pages : 578
Book Description
In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.
Estimation of Dynamic Econometric Models with Errors in Variables
Author: Jaime Terceiro LombaPublisher: Springer Science & Business Media
ISBN: 3642488102
Category : Business & Economics
Languages : en
Pages : 126
Book Description
A new procedure for the maximum-likelihood estimation of dynamic econometric models with errors in both endogenous and exogenous variables is presented in this monograph. A complete analytical development of the expressions used in problems of estimation and verification of models in state-space form is presented. The results are useful in relation not only to the problem of errors in variables but also to any other possible econometric application of state-space formulations.
State-Space Methods for Time Series Analysis
Author: Jose CasalsPublisher: CRC Press
ISBN: 1315362600
Category : Mathematics
Languages : en
Pages : 270
Book Description
The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values. Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form. After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables. Web Resource The authors’ E4 MATLAB® toolbox offers all the computational procedures, administrative and analytical functions, and related materials for time series analysis. This flexible, powerful, and free software tool enables readers to replicate the practical examples in the text and apply the procedures to their own work.
Canonical Auto and Cross Correlations of Multivariate Time Series
Author: Marcia W. BulachPublisher: Universal-Publishers
ISBN: 1581120559
Category : Mathematics
Languages : en
Pages : 418
Book Description
The study of Multivariate Time Series has always been more difficult at the modeling stage than the univariate case. Identification of a suitable model, questions of stability, and the difficulties of prediction are well recognised. A variety of methods appear to be worth examining. This thesis is concerned with the proposal of an useful tool which is to apply canonical analysis to a realisation of a Multivariate Time Series and concentrates it's attention on k-variate ARMA(p, q) models. The multivariate series is partitioned into two overlapping or non-overlapping sets of different sizes. The left set is kept at lag 0 (without loss of generality) and the right set at a sequence of lags s=0,1, ... . The model includes the possibility that the same subset of variables belong to the left set at lag 0 and to the right set at lag s. A technique for dimension reduction is suggested. We tried to elucidate identification and the internal structure of time-dependence at several pairs of lags as a tool for identification. As the technique suggested provide a method of investigation of patterns of interrelations between two multivariate sets or subsets of variables with a joint distribution, it is an efficient tool for use in multivariate series of economic data. A review of the basic models of Multivariate Time Series is given and their canonical auto and cross correlation analysis is presented. In order to study the asymptotic distribution, several Monte Carlo experiments were necessary. We attempted to provide information through simulation about the distributional and other statistical properties for the canonical statistics obtained by our procedures. New software is provided and data experience is given. The first computer program provides us with information, graphs for the canonical auto and cross correlations, test statistics for the 'useful' canonical auto and cross correlations as well as the left and right eigenvectors, left and right intraset and interset matrices of correlations, proportions of variances extracted by the canonical variates of the left and of the right sets and left and right redundancies for lags s=0,1, ... .The second program gives similar calculations for the k-variate ARMA(p, q) models when the matrices of parameters and variance-covariance matrix of the error are known. The third program provides us with the mean value, minimum and maximum values, excess kurtosis, histogram and cumulative distribution for each one of the canonical auto and cross correlations at every lag s calculated from several simulations of Monte Carlo generated k-variate ARMA(p, q) models when the matrices of parameters and variance-covariance matrix of the error are given or when they are generated. The second part of the thesis is devoted to the generalisation of the robust and practically useful univariate Holt-Winters model. We developed formula for the Multivariate Additive Holt-Winters (Seasonal and Non-Seasonal) to the point of application and its reduction to Moving Average form. New software is produced. The link between the two main themes consists on the canonical analysis of a Multivariate Holt-Winters from its reduced MA form and reducing its dimension as well as detecting the basic linear relationships between variables, between and within several lags. We also attempted to investigate the effect of outliers, the removal of non-stationary trends via cubic spline fitting, differencing as well as transformations such as loge (data).
Computational Statistics
Author: Yadolah DodgePublisher: Springer Science & Business Media
ISBN: 3662268116
Category : Business & Economics
Languages : en
Pages : 565
Book Description
The Role of the Computer in Statistics David Cox Nuffield College, Oxford OXIINF, U.K. A classification of statistical problems via their computational demands hinges on four components (I) the amount and complexity of the data, (il) the specificity of the objectives of the analysis, (iii) the broad aspects of the approach to analysis, (ill) the conceptual, mathematical and numerical analytic complexity of the methods. Computational requi rements may be limiting in (I) and (ill), either through the need for special programming effort, or because of the difficulties of initial data management or because of the load of detailed analysis. The implications of modern computational developments for statistical work can be illustrated in the context of the study of specific probabilistic models, the development of general statistical theory, the design of investigations and the analysis of empirical data. While simulation is usually likely to be the most sensible way of investigating specific complex stochastic models, computerized algebra has an obvious role in the more analyti cal work. It seems likely that statistics and applied probability have made insufficient use of developments in numerical analysis associated more with classical applied mathematics, in particular in the solution of large systems of ordinary and partial differential equations, integral equations and integra-differential equations and for the ¢raction of "useful" in formation from integral transforms. Increasing emphasis on models incorporating specific subject-matter considerations is one route to bridging the gap between statistical ana.
Fixed Interval Smoothing for State Space Models
Author: Howard L. WeinertPublisher: Springer Science & Business Media
ISBN: 1461516919
Category : Technology & Engineering
Languages : en
Pages : 126
Book Description
Fixed-interval smoothing is a method of extracting useful information from inaccurate data. It has been applied to problems in engineering, the physical sciences, and the social sciences, in areas such as control, communications, signal processing, acoustics, geophysics, oceanography, statistics, econometrics, and structural analysis. This monograph addresses problems for which a linear stochastic state space model is available, in which case the objective is to compute the linear least-squares estimate of the state vector in a fixed interval, using observations previously collected in that interval. The author uses a geometric approach based on the method of complementary models. Using the simplest possible notation, he presents straightforward derivations of the four types of fixed-interval smoothing algorithms, and compares the algorithms in terms of efficiency and applicability. Results show that the best algorithm has received the least attention in the literature. Fixed Interval Smoothing for State Space Models: includes new material on interpolation, fast square root implementations, and boundary value models; is the first book devoted to smoothing; contains an annotated bibliography of smoothing literature; uses simple notation and clear derivations; compares algorithms from a computational perspective; identifies a best algorithm. Fixed Interval Smoothing for State Space Models will be the primary source for those wanting to understand and apply fixed-interval smoothing: academics, researchers, and graduate students in control, communications, signal processing, statistics and econometrics.
The Dynamics of Business Cycles
Author: Michael ReiterPublisher: Springer Science & Business Media
ISBN: 3642959199
Category : Business & Economics
Languages : en
Pages : 213
Book Description
This study is a revised version of my doctoral dissertation at the Economics Department of the University of Munich. I want to take the opportunity to express my gratitude to some people who have helped me in my work. My greatest thanks go to the supervisor of this dissertation, Professor Claude Billinger. Bis ideas have formed the basis of my work. Be permanently sup ported it with a host of ideas, criticism and encouragement. Furthermore, he provided a stimulating research environment at SEMECON. This study would not have been possible in this form without the help of my present and former colleagues at SEMECON. I am indebted to Rudolf Kohne-Volland, Monika Sebold-Bender and Ulrich Woitek for providing soft ware and guidance for the data analysis. Discussions with them and with Thilo Weser have helped me to take many hurdles, particularly in the early stages of the project. My sincere thanks go to them all. I had the opportunity to present a former version of my growth model at a workshop of Professor Klaus Zimmermann. I want to thank all the parti cipants for their helpful comments. I also acknowledge critical and constructive comments from an anonymous referee. Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Methodology 1. Importance of Stylized Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Limitations of statistical testing. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Evaluating economic models. . . . . . . . . . . . . . . . . . .. . . . 11 . . . . . . 2. Further Methodological Issues . . . . . . . . . . . . . . . . . .. . . . 13 . . . . . .
Time Series Analysis of Irregularly Observed Data
Author: E. ParzenPublisher: Springer Science & Business Media
ISBN: 1468494031
Category : Mathematics
Languages : en
Pages : 372
Book Description
With the support of the Office of Naval Research Program on Statistics and Probability (Dr. Edward J. Wegman, Director), The Department of Statistics at Texas A&M University hosted a Symposium on Time Series Analysis of Irregularly Observed Data during the period February 10-13, 1983. The symposium aimed to provide a review of the state of the art, define outstanding problems for research by theoreticians, transmit to practitioners recently developed algorithms, and stimulate interaction between statisticians and researchers in subject matter fields. Attendance was limited to actively involved researchers. This volume contains refereed versions of the papers presented at the Symposium. We would like to express our appreciation to the many colleagues and staff members whose cheerful help made the Symposium a successful happening which was enjoyed socially and intellectually by all participants. I would like to especially thank Dr. Donald W. Marquardt whose interest led me to undertake to organize this Symposium. This volume is dedicated to the world wide community of researchers who develop and apply methods of statistical analysis of time series. r:;) \J Picture Caption Participants in Symposium on Time Series Analysis of Irregularly Observed Data at Texas A&M University, College Station, Texas, February 10-13, 1983 First Row: Henry L. Gray, D. W. Marquardt, P. M. Robinson, Emanuel Parzen, Julia Abrahams, E. Masry, H. L. Weinert, R. H. Shumway.
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