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This book presents an introduction to linear univariate and
multivariate time series analysis, providing brief theoretical
insights into each topic, and from the beginning illustrating the
theory with software examples. As such, it quickly introduces
readers to the peculiarities of each subject from both theoretical
and the practical points of view. It also includes numerous
examples and real-world applications that demonstrate how to handle
different types of time series data. The associated software
package, SSMMATLAB, is written in MATLAB and also runs on the free
OCTAVE platform. The book focuses on linear time series models
using a state space approach, with the Kalman filter and smoother
as the main tools for model estimation, prediction and signal
extraction. A chapter on state space models describes these tools
and provides examples of their use with general state space models.
Other topics discussed in the book include ARIMA; and transfer
function and structural models; as well as signal extraction using
the canonical decomposition in the univariate case, and VAR, VARMA,
cointegrated VARMA, VARX, VARMAX, and multivariate structural
models in the multivariate case. It also addresses spectral
analysis, the use of fixed filters in a model-based approach, and
automatic model identification procedures for ARIMA and transfer
function models in the presence of outliers, interventions, complex
seasonal patterns and other effects like Easter, trading day, etc.
This book is intended for both students and researchers in various
fields dealing with time series. The software provides numerous
automatic procedures to handle common practical situations, but at
the same time, readers with programming skills can write their own
programs to deal with specific problems. Although the theoretical
introduction to each topic is kept to a minimum, readers can
consult the companion book 'Multivariate Time Series With Linear
State Space Structure', by the same author, if they require more
details.
This book presents a comprehensive study of multivariate time
series with linear state space structure. The emphasis is put on
both the clarity of the theoretical concepts and on efficient
algorithms for implementing the theory. In particular, it
investigates the relationship between VARMA and state space models,
including canonical forms. It also highlights the relationship
between Wiener-Kolmogorov and Kalman filtering both with an
infinite and a finite sample. The strength of the book also lies in
the numerous algorithms included for state space models that take
advantage of the recursive nature of the models. Many of these
algorithms can be made robust, fast, reliable and efficient. The
book is accompanied by a MATLAB package called SSMMATLAB and a
webpage presenting implemented algorithms with many examples and
case studies. Though it lays a solid theoretical foundation, the
book also focuses on practical application, and includes exercises
in each chapter. It is intended for researchers and students
working with linear state space models, and who are familiar with
linear algebra and possess some knowledge of statistics.
This book presents a comprehensive study of multivariate time
series with linear state space structure. The emphasis is put on
both the clarity of the theoretical concepts and on efficient
algorithms for implementing the theory. In particular, it
investigates the relationship between VARMA and state space models,
including canonical forms. It also highlights the relationship
between Wiener-Kolmogorov and Kalman filtering both with an
infinite and a finite sample. The strength of the book also lies in
the numerous algorithms included for state space models that take
advantage of the recursive nature of the models. Many of these
algorithms can be made robust, fast, reliable and efficient. The
book is accompanied by a MATLAB package called SSMMATLAB and a
webpage presenting implemented algorithms with many examples and
case studies. Though it lays a solid theoretical foundation, the
book also focuses on practical application, and includes exercises
in each chapter. It is intended for researchers and students
working with linear state space models, and who are familiar with
linear algebra and possess some knowledge of statistics.
This book presents an introduction to linear univariate and
multivariate time series analysis, providing brief theoretical
insights into each topic, and from the beginning illustrating the
theory with software examples. As such, it quickly introduces
readers to the peculiarities of each subject from both theoretical
and the practical points of view. It also includes numerous
examples and real-world applications that demonstrate how to handle
different types of time series data. The associated software
package, SSMMATLAB, is written in MATLAB and also runs on the free
OCTAVE platform. The book focuses on linear time series models
using a state space approach, with the Kalman filter and smoother
as the main tools for model estimation, prediction and signal
extraction. A chapter on state space models describes these tools
and provides examples of their use with general state space models.
Other topics discussed in the book include ARIMA; and transfer
function and structural models; as well as signal extraction using
the canonical decomposition in the univariate case, and VAR, VARMA,
cointegrated VARMA, VARX, VARMAX, and multivariate structural
models in the multivariate case. It also addresses spectral
analysis, the use of fixed filters in a model-based approach, and
automatic model identification procedures for ARIMA and transfer
function models in the presence of outliers, interventions, complex
seasonal patterns and other effects like Easter, trading day, etc.
This book is intended for both students and researchers in various
fields dealing with time series. The software provides numerous
automatic procedures to handle common practical situations, but at
the same time, readers with programming skills can write their own
programs to deal with specific problems. Although the theoretical
introduction to each topic is kept to a minimum, readers can
consult the companion book 'Multivariate Time Series With Linear
State Space Structure', by the same author, if they require more
details.
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