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Title:

Theoretical Foundations of Autoregressive Models for Time Series on Acyclic Directed Graphs

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Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as ...

Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as the sum of averages over the sub-intervals implies linear restrictions in the tree-structured model. Under a white noise assumption for transition and observation noise there is an change-of-resolution Kalman filter for linear least squares prediction of interval averages (Chou 1991). This class of models is generalized by modeling transition noise on the same scale in linear state space form. The third class deals with models on a more general class of directed acyclic graphs where nodes are allowed to have two parents. We show that these models have a linear state space representation with white system and coloured observation noise. Key words: linear least squares prediction, tree-structured model, mass-balance, acyclic directed graph, linear state space model, linear Kalman filter, score vector. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper326.pdf

http://www-m4.mathematik.tu-muenchen.de/m4/Papers/Czado/paper326.pdf Minimize

Document Type:

text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Multiresolution Analysis of Long Time Series With Applications to Finance

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We consider multi-resolution time series models and their application to high-frequency fi-nancial data. An individual transaction share price of a specific firm is subject to market mi-crostructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolu...

We consider multi-resolution time series models and their application to high-frequency fi-nancial data. An individual transaction share price of a specific firm is subject to market mi-crostructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolution and averaging over shorter intervals lead to a finer resolution. Arranging sub-intervals of given lengths on scales with coarse to fine resolution imply a structure which can be represented as a directed acyclic graph. Time series models are then formulated using this graph structure. It is shown that these models have a linear state space representation which allows for efficient computation of the likelihood needed in parameter estimation and for a straightforward treatment of missing observations. Application of these models to the log transaction prices of the IBM shares traded at the New York Stock Exchange from February until October 2002 show that the corresponding one-step prediction er-rors are heavy tailed and therefore a specific variance term is allowed to follow a fiEGARCH specification, improving the tail behavior and leading to a better fit. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.ma.tum.de/Papers/Czado/hoegn.pdf

http://www-m4.ma.tum.de/Papers/Czado/hoegn.pdf Minimize

Document Type:

text

Language:

en

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1

1 Minimize

DDC:

330 Economics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Theoretical Foundations of Autoregressive Models for Time Series on Acyclic Directed Graphs

Description:

Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as ...

Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as the sum of averages over the sub-intervals implies linear restrictions in the tree-structured model. Under a white noise assumption for transition and observation noise there is an change-of-resolution Kalman filter for linear least squares prediction of interval averages (Chou 1991). This class of models is generalized by modeling transition noise on the same scale in linear state space form. The third class deals with models on a more general class of directed acyclic graphs where nodes are allowed to have two parents. We show that these models have a linear state space representation with white system and coloured observation noise. Minimize

Year of Publication:

2003

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310 ; linear least squares prediction ; tree-structured model ; mass-balance ; acyclic directed graph ; linear state space model ; linear Kalman filter

ddc:310 ; linear least squares prediction ; tree-structured model ; mass-balance ; acyclic directed graph ; linear state space model ; linear Kalman filter Minimize

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http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion papers / Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 326

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Title:

Multiresolution analysis of long time series with applications to finance

Description:

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resoluti...

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolution and averaging over shorter intervals lead to a finer resolution. Arranging sub-intervals of given lengths on scales with coarse to fine resolution imply a structure which can be represented as a directed acyclic graph. Time series models are then formulated using this graph structure. It is shown that these models have a linear state space representation which allows for efficient computation of the likelihood needed in parameter estimation and for a straightforward treatment of missing observations. Application of these models to the log transaction prices of the IBM shares traded at the New York Stock Exchange from February until October 2002 show that the corresponding one-step prediction errors are heavy tailed and therefore a specific variance term is allowed to follow a fiEGARCH specification, improving the tail behavior and leading to a better fit. Minimize

Publisher:

Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2005

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310 ; multiresolution ; time series ; state space representation ; colored transition noise ; directed acyclic graphs

ddc:310 ; multiresolution ; time series ; state space representation ; colored transition noise ; directed acyclic graphs Minimize

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Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 497

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Title:

Multiresolution Analysis of Long Time Series with Applications to Finance

Description:

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resoluti...

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolution and averaging over shorter intervals lead to a finer resolution. Arranging sub-intervals of given lengths on scales with coarse to fine resolution imply a structure which can be represented as a directed acyclic graph. Time series models are then formulated using this graph structure. It is shown that these models have a linear state space representation which allows for efficient computation of the likelihood needed in parameter estimation and for a straightforward treatment of missing observations. Application of these models to the log transaction prices of the IBM shares traded at the New York Stock Exchange from February until October 2002 show that the corresponding one-step prediction errors are heavy tailed and therefore a specific variance term is allowed to follow a fiEGARCH specification, improving the tail behavior and leading to a better fit. Minimize

Year of Publication:

2006-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

330 Economics *(computed)*

Relations:

http://epub.ub.uni-muenchen.de/1864/1/paper_497.pdf ; Högn, Ralph und Czado, Claudia (2006): Multiresolution Analysis of Long Time Series with Applications to Finance. Sonderforschungsbereich 386, Discussion Paper 497

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Title:

Theoretical Foundations of Autoregressive Models for Time Series on Acyclic Directed Graphs

Description:

Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as ...

Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as the sum of averages over the sub-intervals implies linear restrictions in the tree-structured model. Under a white noise assumption for transition and observation noise there is an change-of-resolution Kalman filter for linear least squares prediction of interval averages \shortcite{chou:1991}. This class of models is generalized by modeling transition noise on the same scale in linear state space form. The third class deals with models on a more general class of directed acyclic graphs where nodes are allowed to have two parents. We show that these models have a linear state space representation with white system and coloured observation noise. Minimize

Year of Publication:

2003-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

Relations:

http://epub.ub.uni-muenchen.de/1705/1/paper_326.pdf ; Högn, Ralph und Czado, Claudia (2003): Theoretical Foundations of Autoregressive Models for Time Series on Acyclic Directed Graphs. Sonderforschungsbereich 386, Discussion Paper 326

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