Publications
NIBIOs employees contribute to several hundred scientific articles and research reports every year. You can browse or search in our collection which contains references and links to these publications as well as other research and dissemination activities. The collection is continously updated with new and historical material.
2008
Authors
Lukas Gudmundsson Holger LangeAbstract
Many time series analysis methods depend on equally spaced observations with no data point missing. If this condition is met, powerful techniques are available that identify temporal structures such as trends, periodic phenomena or nonlinear dynamics. Unfortunately, most observations of natural systems, in particular over longer periods of time such as decades, are prone to sampling errors leading to missing points in the observations. Singular System Analysis (SSA) is a powerful tool to extract the dynamics contained in time series at arbitrary temporal scales. In its original formulation, however, SSA relies as well on data without missing values. Recently several extensions to SSA have been proposed which are designed to fill the gaps, exploiting the dynamics contained in the sampled parts of the series to estimate the structure of the signal at the position of missing values. SSA consists of two steps: Decomposition and reconstruction. For the decomposition the time series under investigation is embedded into a trajectory matrix and decomposed with singular value decomposition. The reconstruction (of selected components) of the time series employs the left and right singular values to obtain additive components of the time series. In the original variant of SSA both steps are dependent on gap free data sets. In order to evaluate the power of SSA for time series with missing values we simulate 1000 series of different processes - ARMA(2,3) and red noise contaminated sine waves. Several gap–schemes (continuous, periodic, and uniformly distributed) are used to create time series with up to 50% (artificially) missing values. SSA is applied on all surrogate series. The decomposition as well as the reconstruction is compared systematically to the gap free benchmark. In addition we evaluate the ability of SSA to capture periodic phenomena in the presence of missing values and whether periodical gaps lead to the identification of spurious periods. We demonstrate that SSA successfully reproduces the signal part of time series (i.e. components with large eigenvalues) for up to 30% missing values. For less significant components with higher rank numbers, the presence of gaps is increasingly deleterious. A number of distributed smaller gaps, a situation most likely to occur in observations, spoils the analysis to a much lesser degree than a single large gap. Thus, these new variants of SSA substantially enlarge the set of observational time series amenable to the analysis, and allows for obtaining precise estimates of the signal at the position of missing data points.
Authors
Marit Almvik Gunnhild Riise Randi Bolli Agnethe Christiansen Sven R. Odenmarck Trond Børresen Cathrine Waage TveitAbstract
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Authors
Bjørn Molteberg Trygve S. Aamlid Gudni Thorvaldsson Anders Hammarlund Frank Enger Jan Tangsveen Trond Olav Pettersen Daniel NordAbstract
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Authors
David Bredström Patrik Flisberg Mikael RönnqvistAbstract
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Authors
Tore SkrøppaAbstract
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Authors
Kathrine Høybakk Anita Tøsse T. Nilsen Silje Engdal Bent Håvard Hellum Jens Rohloff Mette Thomsen Odd Georg NilsenAbstract
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Authors
Trond Rafoss Arild Sletten Leif SundheimAbstract
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