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Assessing direct and indirect seasonal adjustment in state space - a comparison between ordinary and optimal approaches
Stockholm University, Faculty of Social Sciences, Department of Statistics.
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2013 (English)Report (Other academic)
Abstract [en]

The problem of whether seasonal adjustment should be used prior to or after aggregation of time series is quite old. We tackle the problem using the state space representation and the variance/covariance structure. The variances of the estimated components are compared for direct and indirect adjustment and also to the optimal adjustment method. The covariance structure between the time series is important for the relative efficiency. Indirect adjustment is always best when the series are independent, but when the series or the measurement errors are negatively correlated, direct estimation may be much better in the above sense. Some covariance structures indicate that direct adjustment should be used while others indicate that indirect approaches are more efficient. Signal to noise ratios and relative variances are used for inference.

Place, publisher, year, edition, pages
Stockholm, 2013. , 24 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 2013:1
Keyword [en]
covariance, signal to noise, efficiency, indirect seasonal adjustment
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-89235OAI: oai:DiVA.org:su-89235DiVA: diva2:616537
Available from: 2013-04-17 Created: 2013-04-17 Last updated: 2014-04-01Bibliographically approved
In thesis
1. Seasonal Adjustment and Dynamic Linear Models
Open this publication in new window or tab >>Seasonal Adjustment and Dynamic Linear Models
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Dynamic Linear Models are a state space model framework based on the Kalman filter. We use this framework to do seasonal adjustments of empirical and artificial data. A simple model and an extended model based on Gibbs sampling are used and the results are compared with the results of a standard seasonal adjustment method. The state space approach is then extended to discuss direct and indirect seasonal adjustments. This is achieved by applying a seasonal level model with no trend and some specific input variances that render different signal-to-noise ratios. This is illustrated for a system consisting of two artificial time series. Relative efficiencies between direct, indirect and multivariate, i.e. optimal, variances are then analyzed. In practice, standard seasonal adjustment packages do not support optimal/multivariate seasonal adjustments, so a univariate approach to simultaneous estimation is presented by specifying a Holt-Winters exponential smoothing method. This is applied to two sets of time series systems by defining a total loss function that is specified with a trade-off weight between the individual series’ loss functions and their aggregate loss function. The loss function is based on either the more conventional squared errors loss or on a robust Huber loss. The exponential decay parameters are then estimated by minimizing the total loss function for different trade-off weights. It is then concluded what approach, direct or indirect seasonal adjustment, is to be preferred for the two time series systems. The dynamic linear modeling approach is also applied to Swedish political opinion polls to assert the true underlying political opinion when there are several polls, with potential design effects and bias, observed at non-equidistant time points. A Wiener process model is used to model the change in the proportion of voters supporting either a specific party or a party block. Similar to stock market models, all available (political) information is assumed to be capitalized in the poll results and is incorporated in the model by assimilating opinion poll results with the model through Bayesian updating of the posterior distribution. Based on the results, we are able to assess the true underlying voter proportion and additionally predict the elections.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2013. 8 p.
Keyword
Dynamic linear models, DLM, direct and indirect seasonal adjustment, relative efficiency, Huber loss function, Polls of polls, Wiener process, Swedish elections
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-89496 (URN)978-91-7447-678-1 (ISBN)
Public defence
2013-06-12, DeGeersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of doctoral defence the following papers were unpublished and had a status as follows: Paper 3: Manuscript; Paper 4: Manuscripts

Available from: 2013-05-16 Created: 2013-04-27 Last updated: 2013-04-29Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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