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Seasonal Adjustment and Dynamic Linear Models
Stockholm University, Faculty of Social Sciences, Department of Statistics.
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 [en]
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: urn:nbn:se:su:diva-89496ISBN: 978-91-7447-678-1 (print)OAI: oai:DiVA.org:su-89496DiVA: diva2:618497
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
List of papers
1. A Comparison of Seasonal Adjustment Methods: Dynamic Linear Models versus TRAMO/SEATS
Open this publication in new window or tab >>A Comparison of Seasonal Adjustment Methods: Dynamic Linear Models versus TRAMO/SEATS
2013 (English)Report (Other academic)
Abstract [en]

Seasonal adjustment can be done in the state space framework by Dynamic Linear Models. This approach is compared with seasonal adjustment by TRAMO/SEATS. The comparison uses simulated time series and real Swedish foreign trade data, the latter allowing a discussion on the consistency issue in aggregation, i.e. direct versus indirect seasonal adjustment. We start by a simple dynamic model and then increase the model structure using Gibbs sampling to identify coefficients for the state evolution matrix. Our empirical study shows that the simpler state spate approach exaggerates seasonal adjustment while the extended model with sampled coefficients may offer a tool for seasonal adjustment. For simulated data, we find that TRAMO/SEATS is better than the state space approach.

Publisher
22 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 2013:2
Keyword
Dynamic Linear Models, DLM, seasonal adjustment, consistency, foreign trade
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-89141 (URN)
Available from: 2013-04-18 Created: 2013-04-13 Last updated: 2014-04-01Bibliographically approved
2. Assessing direct and indirect seasonal adjustment in state space - a comparison between ordinary and optimal approaches
Open this publication in new window or tab >>Assessing direct and indirect seasonal adjustment in state space - a comparison between ordinary and optimal approaches
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
covariance, signal to noise, efficiency, indirect seasonal adjustment
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-89235 (URN)
Available from: 2013-04-17 Created: 2013-04-17 Last updated: 2014-04-01Bibliographically approved
3. A Note on the Trade-off between Direct and Indirect Seasonal Adjustments
Open this publication in new window or tab >>A Note on the Trade-off between Direct and Indirect Seasonal Adjustments
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Direct and indirect seasonal adjustments can be viewed as opposite formulations of an error minimization problem that occurs when seasonally adjusting a system of time series. In this study, a loss function is formulated that is a weighted combination of the errors of the input time series and the aggregate error. Holt-Winters’ exponential smoothing methods on squared error loss functions or robust Huber loss functions are applied to quarterly Swedish GDP and monthly foreign trade data. All input series are seasonally adjusted jointly but still univariately and trade-off point between direct and indirect seasonal adjustments are estimated. The quadratic loss function is found to cause larger differences between direct and indirect seasonal adjustments than the Huber loss function does. Results indicate that pure indirect seasonal adjustment should be avoided for GDP and pure direct seasonal adjustment should be avoided for foreign trade. Adjustments in between with a combined loss function seem to work well for all purposes.

Keyword
direct/indirect seasonal adjustment, Huber loss function, exponential smoothing, trade-off
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-89347 (URN)
Available from: 2013-04-22 Created: 2013-04-22 Last updated: 2013-04-29
4. Combination of sample surveys and projections of political opinions
Open this publication in new window or tab >>Combination of sample surveys and projections of political opinions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In Sweden, political party preferences are surveyed almost every month by several institutes. The sample sizes are usually between 1000 and 2000 individuals, which means that the standard deviations are between 1 and 1.5 %. We study how these estimates can be improved by combining them and by modelling the behaviour over time. Our model is a combination of a dynamic model based on Wiener processes and sampling theory with design effects and measurement biases. The variances of our estimates are about 1/3 of those of the original polls when only previous polls are used and about 1/5 if the information in later polls is included. The proposed method leads to a smaller bias since the institute biases can be estimated. The party preferences are modelled as random processes, making it possible to study the probability for events like a party (or block) getting more than 50 % of the political preferences. Assuming that the same model will hold in the future, we can present intervals for future election results.

National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:su:diva-89314 (URN)
Available from: 2013-04-21 Created: 2013-04-21 Last updated: 2013-04-29

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