## 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

## 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

## 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