## 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

## 9 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

## 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

## More is not always better: Kalman filtering in dynamic factor models

*Pilar Poncela and Esther Ruiz*

### in Unobserved Components and Time Series Econometrics

- Published in print:
- 2015
- Published Online:
- January 2016
- ISBN:
- 9780199683666
- eISBN:
- 9780191763298
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199683666.003.0011
- Subject:
- Economics and Finance, Econometrics

For dynamic factor models the relationship between the mean square error of the Kalman filter estimator of the underlying factors and the number of variables in the model is established. It is shown ... 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

## Modeling Producer Behavior

*Dale W. Jorgenson, Richard J. Goettle, Mun S. Ho, and Peter J. Wilcoxen*

### in Double Dividend: Environmental Taxes and Fiscal Reform in the United States

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262027090
- eISBN:
- 9780262318563
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262027090.003.0004
- Subject:
- Economics and Finance, Development, Growth, and Environmental

Production functions in many CGE models use a nest of CES functions which imposes a strong assumption about substitution patterns. Here we describe the implementation of a more flexible translog ... More

## Linear-Gaussian systems and signal processing

*Max A. Little*

### in Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198714934
- eISBN:
- 9780191879180
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198714934.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy, Mathematical Physics

Linear systems theory, based on the mathematics of vector spaces, is the backbone of all “classical” DSP and a large part of statistical machine learning. The basic idea -- that linear algebra ... More

## Data modeling

*Joseph F. Boudreau and Eric S. Swanson*

### in Applied Computational Physics

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0016
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A variety of techniques for extracting information from data are presented, from pedestrian approaches such as the centuries old linear least-squares fit, to elegant binned and unbinned likelihood ... More

## Martingale unobserved component models

*Neil Shephard*

### in Unobserved Components and Time Series Econometrics

- Published in print:
- 2015
- Published Online:
- January 2016
- ISBN:
- 9780199683666
- eISBN:
- 9780191763298
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199683666.003.0010
- Subject:
- Economics and Finance, Econometrics

This chapter generalizes the familiar linear Gaussian unobserved component models or structural time series models to martingale unobserved component models. This generates forecasts whose rate of ... More

## Particle filters for the geosciences

*P. J. van Leeuwen*

### 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/9780198723844.003.0013
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

This chapter, compares results from the Canadian global ensemble Kalman filter (EnKF) with observations. This inevitably leads to discrepancies between the observed real atmosphere and its modelled ... More

## Smoothers

*E. Cosme*

### 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/9780198723844.003.0004
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

This chapter describes the use of smoothers in data assimilation. The filtering problem in data assimilation consists in estimating the state of a system based on past and present observations. In ... More

## Error dynamics in ensemble Kalman-filter systems: localization

*P. Houtekamer*

- Published in print:
- 2014
- Published Online:
- March 2015
- ISBN:
- 9780198723844
- eISBN:
- 9780191791185
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198723844.003.0010
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics

In this chapter, an experimental environment built around the Lorenz III toy model is used to demonstrate some points concerning localization. In an ensemble Kalman filter, localization is almost ... More

## Sovereign Credit Risk in Latin America and Global Common Factors

*Manuel Agosin and Juan Díaz-Maureira*

### in Macroeconomics and Development: Roberto Frenkel and the Economics of Latin America

- Published in print:
- 2016
- Published Online:
- September 2016
- ISBN:
- 9780231175081
- eISBN:
- 9780231541213
- Item type:
- chapter

- Publisher:
- Columbia University Press
- DOI:
- 10.7312/columbia/9780231175081.003.0016
- Subject:
- Economics and Finance, Macro- and Monetary Economics

the chapter studies the importance of global common factors in the evolution of sovereign credit risk in emerging economies between 2007 and 2012. Using principal component analysis and Kalman ... More

## Learning

*Kerry E. Back*

### in Asset Pricing and Portfolio Choice Theory

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190241148
- eISBN:
- 9780190241179
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190241148.003.0023
- Subject:
- Economics and Finance, Financial Economics

Continuous‐time filtering is explained, including the Kalman filter and filtering for a Markov chain with hidden states. Filtering theory is applied to analyze portfolio choice and equilibrium asset ... More