Statistical Software for State Space Methods
In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed...
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doaj-4e363cdad8714058a0ee8ffde5571cd12020-11-24T21:28:38ZengFoundation for Open Access StatisticsJournal of Statistical Software1548-76602011-05-014101Statistical Software for State Space MethodsJacques J. F. CommandeurSiem Jan KoopmanMarius OomsIn this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume.http://www.jstatsoft.org/v41/i01/paperARMA modelKalman filterstate space methodsunobserved componentssoftware tools |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jacques J. F. Commandeur Siem Jan Koopman Marius Ooms |
spellingShingle |
Jacques J. F. Commandeur Siem Jan Koopman Marius Ooms Statistical Software for State Space Methods Journal of Statistical Software ARMA model Kalman filter state space methods unobserved components software tools |
author_facet |
Jacques J. F. Commandeur Siem Jan Koopman Marius Ooms |
author_sort |
Jacques J. F. Commandeur |
title |
Statistical Software for State Space Methods |
title_short |
Statistical Software for State Space Methods |
title_full |
Statistical Software for State Space Methods |
title_fullStr |
Statistical Software for State Space Methods |
title_full_unstemmed |
Statistical Software for State Space Methods |
title_sort |
statistical software for state space methods |
publisher |
Foundation for Open Access Statistics |
series |
Journal of Statistical Software |
issn |
1548-7660 |
publishDate |
2011-05-01 |
description |
In this paper we review the state space approach to time series analysis and establish the notation that is adopted in this special volume of the Journal of Statistical Software. We first provide some background on the history of state space methods for the analysis of time series. This is followed by a concise overview of linear Gaussian state space analysis including the modelling framework and appropriate estimation methods. We discuss the important class of unobserved component models which incorporate a trend, a seasonal, a cycle, and fixed explanatory and intervention variables for the univariate and multivariate analysis of time series. We continue the discussion by presenting methods for the computation of different estimates for the unobserved state vector: filtering, prediction, and smoothing. Estimation approaches for the other parameters in the model are also considered. Next, we discuss how the estimation procedures can be used for constructing confidence intervals, detecting outlier observations and structural breaks, and testing model assumptions of residual independence, homoscedasticity, and normality. We then show how ARIMA and ARIMA components models fit in the state space framework to time series analysis. We also provide a basic introduction for non-Gaussian state space models. Finally, we present an overview of the software tools currently available for the analysis of time series with state space methods as they are discussed in the other contributions to this special volume. |
topic |
ARMA model Kalman filter state space methods unobserved components software tools |
url |
http://www.jstatsoft.org/v41/i01/paper |
work_keys_str_mv |
AT jacquesjfcommandeur statisticalsoftwareforstatespacemethods AT siemjankoopman statisticalsoftwareforstatespacemethods AT mariusooms statisticalsoftwareforstatespacemethods |
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1725969330727813120 |