Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models
This article presents a new exact solution for the initialization of the Kalman filter for state space models with diffuse initial conditions. For example, the regression model with stochastic trend, seasonal and other nonstationary autoregressive integrated moving average components requires a (par...
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| Veröffentlicht in: | Journal of the American Statistical Association 1997-12, Vol.92 (440), p.1630-1638 |
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| container_title | Journal of the American Statistical Association |
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| creator | Koopman, Siem Jan |
| description | This article presents a new exact solution for the initialization of the Kalman filter for state space models with diffuse initial conditions. For example, the regression model with stochastic trend, seasonal and other nonstationary autoregressive integrated moving average components requires a (partially) diffuse initial state vector. The proposed analytical solution is easy to implement and computationally efficient. The exact solution for smoothing is also given. Missing observations are handled in a straightforward manner. All proofs rely on elementary results. |
| doi_str_mv | 10.1080/01621459.1997.10473685 |
| format | Article |
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All proofs rely on elementary results.</description><identifier>ISSN: 0162-1459</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1080/01621459.1997.10473685</identifier><identifier>CODEN: JSTNAL</identifier><language>eng</language><publisher>Alexandria, VA: Taylor & Francis Group</publisher><subject>Autoregressive integrated moving average component models ; Covariance matrices ; Data smoothing ; Diffuse initial conditions ; Exact sciences and technology ; Inference from stochastic processes; time series analysis ; Kalman filters ; Likelihood function and score vector ; Mathematical analysis ; Mathematical models ; Mathematical vectors ; Mathematics ; Matrices ; Missing observations ; Probability and statistics ; Regression analysis ; Sciences and techniques of general use ; Seasonality ; Spatial dimension ; State space ; State vectors ; Statistical analysis ; Statistical variance ; Statistics ; Stochastic models ; Theory and Methods ; Time series ; Time series models</subject><ispartof>Journal of the American Statistical Association, 1997-12, Vol.92 (440), p.1630-1638</ispartof><rights>Copyright Taylor & Francis Group, LLC 1997</rights><rights>Copyright 1997 American Statistical Association</rights><rights>1998 INIST-CNRS</rights><rights>Copyright American Statistical Association Dec 1997</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c467t-1d21cd8100e0b4e6803f76f9321c19c8dc831e6edaa117f542ce62f411708f03</citedby><cites>FETCH-LOGICAL-c467t-1d21cd8100e0b4e6803f76f9321c19c8dc831e6edaa117f542ce62f411708f03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2965434$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2965434$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27846,27901,27902,57992,57996,58225,58229,59620,60409</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2107611$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Koopman, Siem Jan</creatorcontrib><title>Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models</title><title>Journal of the American Statistical Association</title><description>This article presents a new exact solution for the initialization of the Kalman filter for state space models with diffuse initial conditions. For example, the regression model with stochastic trend, seasonal and other nonstationary autoregressive integrated moving average components requires a (partially) diffuse initial state vector. The proposed analytical solution is easy to implement and computationally efficient. The exact solution for smoothing is also given. Missing observations are handled in a straightforward manner. All proofs rely on elementary results.</description><subject>Autoregressive integrated moving average component models</subject><subject>Covariance matrices</subject><subject>Data smoothing</subject><subject>Diffuse initial conditions</subject><subject>Exact sciences and technology</subject><subject>Inference from stochastic processes; time series analysis</subject><subject>Kalman filters</subject><subject>Likelihood function and score vector</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical vectors</subject><subject>Mathematics</subject><subject>Matrices</subject><subject>Missing observations</subject><subject>Probability and statistics</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>Seasonality</subject><subject>Spatial dimension</subject><subject>State space</subject><subject>State vectors</subject><subject>Statistical analysis</subject><subject>Statistical 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Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models</title><author>Koopman, Siem Jan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c467t-1d21cd8100e0b4e6803f76f9321c19c8dc831e6edaa117f542ce62f411708f03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Autoregressive integrated moving average component models</topic><topic>Covariance matrices</topic><topic>Data smoothing</topic><topic>Diffuse initial conditions</topic><topic>Exact sciences and technology</topic><topic>Inference from stochastic processes; time series analysis</topic><topic>Kalman filters</topic><topic>Likelihood function and score vector</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematical vectors</topic><topic>Mathematics</topic><topic>Matrices</topic><topic>Missing observations</topic><topic>Probability and 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| identifier | ISSN: 0162-1459 |
| ispartof | Journal of the American Statistical Association, 1997-12, Vol.92 (440), p.1630-1638 |
| issn | 0162-1459 1537-274X |
| language | eng |
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| source | Jstor Complete Legacy; Taylor & Francis Journals Complete; Periodicals Index Online; JSTOR Mathematics & Statistics |
| subjects | Autoregressive integrated moving average component models Covariance matrices Data smoothing Diffuse initial conditions Exact sciences and technology Inference from stochastic processes time series analysis Kalman filters Likelihood function and score vector Mathematical analysis Mathematical models Mathematical vectors Mathematics Matrices Missing observations Probability and statistics Regression analysis Sciences and techniques of general use Seasonality Spatial dimension State space State vectors Statistical analysis Statistical variance Statistics Stochastic models Theory and Methods Time series Time series models |
| title | Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models |
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