A key text - the W&H book:
Bayesian Forecasting and
Dynamic Models (2nd Ed.) by Mike West and Jeff Harrison
Here it is at
Amazon
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2002 Valencia overview/tutorial on Bayesian time series
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An older overview/tutorial (AIstats97) slide set, that includes additional
commentary on mixture modelling (multiprocess models) in time series, and other topics
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STA 214 notes from the
Fall 2004 STA 214
class, that includes a great deal of development of basic ideas, theory and methods
of univariate AR time series AR(1) models, including key model decompositions ideas and methods,
state-space versions, and the detailed development of univariate
stochastic volatility models, among other things. See Sections 1,2,3, 4.6, 10,12,13.
The STA 214 site also contains much more on the Schedule and Support pages - including a heap of
(potentially) useful Matlab code and examples.
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Draft chapters from a new time series monograph in preparation (Raquel Prado and Mike West).
See Chapter 1 for introductory/general material on time series, especially standard stationary models.
More may be added later.
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Papers and book chapters that will be relevant in the course, and that also
may be of interest in connection with course projects, include:
- O. Aguilar and M. West (2000)
Bayesian dynamic factor models and variance matrix discounting for portfolio allocation.
Journal of Business and Economic Statistics, 18, 338-357.
- Chapter 12 of W&H: Multi-Process models - mixture models in sequential analysis of time series
- AR and TVAR decompositions (W&H sections 9.5, 9.6, 15.3), applied in EEG studies:
- Prado et al (1999)
Evaluation and comparison of EEG traces: Latent structure in non-stationary time series,
Journal of the American Statistical Association, 94, 1083-1095; and
- related developments in multivariate time series in
Prado and West (1997)
Exploratory modelling of multiple non-stationary time series:
Latent process structure and decompositions,
in Modelling Longitudinal and Spatially Correlated Data,
(ed: T. Gregoire), Springer-Verlag, and also related models - and
- other multivariate time series modelling ideas - in
Prado, Krystal and West (2001)
Multi-channel EEG analyses via dynamic regression models with time-varying lag/lead structure,
JRSS (C)50 95-110.
- Particle filtering: sequential learning and updating in dynamic models for time series and
signal processing - methodology of particle filtering is used in works (such as Aguilar and West above)
in finance and in communications, speech processing, etc and is a hot-topic in research: the 2000
multi-author book
Sequential Monte Carlo Methods in Practice
- there are copies in Duke Statistics - has a number of interesting chapters that could form the basis of projects
on this (challenging) topic. There are connections with mixture models in time series and many other
relevant areas of the field.
Here's a useful web resources on the general topic: the
particle filtering group site, and
a recent paper on particle filtering and smoothing which, in addition to some nice speech processing
examples, is a good overview/intro :
Godsill et al (2004)
Monte Carlo smoothing for non-linear time series,
Journal of the American Statistical Association, 99, 156-168.
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Project topics:
- Application of DLMs and time series analysis methods in a (very) substantive application
- in your own area of research interest. This may be is particular interest if
you have research ongoing that is generating an interest in time series and dynamic modelling
methodologies. Little projects with limited or no data will not qualify.
- Computation and analysis of subset AR and TVAR models.
- Develop efficient MCMC code for subset regression variable uncertainty using
standard mixture models - batch processing.
- Sequential processing - Multi-Process I model context.
- TVAR models - research frontier project.
- Theory/concepts: High-(maximum) order AR or TVAR model inversion to ARMA, TVARMA.
- Develop and implement Multi-Process Class II models for outlier and change-point detection
in a specified class of DLMs: focus on development of expanding mixtures of time series models.
- Development of particle filtering method for sequential simulation-based analysis of
specified class of DLMs, such as simplified multivariate volatility models.
- Higher-order stochastic volatility models and components of volatility processes.
- Experiments in implementations on cluster computers in any of the above.
- Development of time series decompositions theory and methods in multivariate settings,
including investigation of decompositions of multiple univariate series "driven"
by an underlying AR process.
- Any serious methodological/computational development topic you suggest and discuss
with me, and that I approve.
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