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Thiele: Pioneer in Statistics

Steffen L. Lauritzen

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509721
eISBN:
9780191709197
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509721.001.0001
Subject:
Mathematics, Probability / Statistics

Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private ... More


Time Series Analysis by State Space Methods: Second Edition

James Durbin and Siem Jan Koopman

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.001.0001
Subject:
Mathematics, Probability / Statistics

This book presents a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as ... More


Introduction to the Kalman filter

C. Snyder

in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198723844
eISBN:
9780191791185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198723844.003.0003
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter introduces The Kalman filter, which implements Bayesian data assimilation for linear, Gaussian systems. Its update equations can also be derived as the best linear unbiased estimator ... More


Filtering, smoothing and forecasting

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter begins with a set of four lemmas from elementary multivariate regression which provides the essentials of the theory for the general linear state space model from both a classical and a ... More


Initialisation of filter and smoother

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0005
Subject:
Mathematics, Probability / Statistics

Computational algorithms in state space analyses are mainly based on recursions, that is, formulae in which the value at time t + 1 is calculated from earlier values for t, t − 1, …, 1. This chapter ... More


Time‐varying parameters and state space models

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0009
Subject:
Economics and Finance, Econometrics

Linear state space models have become popular in time series, and there are applications to many fields. The Kalman filter is often a fundamental tool. In this chapter it is shown that there are ... More


On the application of the method of least squares to some cases, in which a combination of certain types of inhomogeneous random sources of errors gives these a ‘systematic’ character

T. N. Thiele

in Thiele: Pioneer in Statistics

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509721
eISBN:
9780191709197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509721.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter presents Thiele's first paper on the method of least squares. This paper was so far ahead of its time that only a few appreciated the results. Thiele's recursive algorithm developed in ... More


Unobserved Components and Time Series Econometrics

Siem Jan Koopman and Neil Shephard (eds)

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.001.0001
Subject:
Economics and Finance, Econometrics

This book is a tribute to Professor Andrew Harvey, who has been an active researcher for four decades, writing on many aspects of time series modeling with a particular focus on economic and more ... More


Combining Particle Filters with SMC Samplers

Edward P. Herbst and Frank Schorfheide

in Bayesian Estimation of DSGE Models

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691161082
eISBN:
9781400873739
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161082.003.0010
Subject:
Economics and Finance, Econometrics

This chapter combines the SMC algorithm with the particle filter approximation of the likelihood function to develop an SMC2 algorithm. As with the PFMH algorithm, the goal is to obtain a posterior ... More


Optimal Control Theory

Emanuel Todorov

in Bayesian Brain: Probabilistic Approaches to Neural Coding

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262042383
eISBN:
9780262294188
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262042383.003.0012
Subject:
Neuroscience, Disorders of the Nervous System

Optimal control theory is a mathematical discipline for studying the neural control of movement. This chapter presents a mathematical introduction to optimal control theory and discusses the ... More


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