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Structural time series models and the Kalman filter: a concise review

Author

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  • Joao Tovar Jalles
Abstract
The continued increase in availability of economic data in recent years and, more importantly, the possibility to construct larger frequency time series, have fostered the use (and development) of statistical and econometric techniques to treat them more accurately. This paper presents an exposition of structural time series models by which a time series can be decomposed as the sum of a trend, seasonal and irregular components. In addition to a detailled analysis of univariate speci?cations we also address the SUTSE multivariate case and the issue of cointegration. Finally, the recursive estimation and smoothing by means of the Kalman ?lter algorithm is described taking into account its di¤erent stages, from initialisation to parameters estimation.

Suggested Citation

  • Joao Tovar Jalles, 2009. "Structural time series models and the Kalman filter: a concise review," Nova SBE Working Paper Series wp541, Universidade Nova de Lisboa, Nova School of Business and Economics.
    • Handle: RePEc:unl:unlfep:wp541
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    File URL: https://run.unl.pt/bitstream/10362/11569/1/wp541.pdf
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    References listed on IDEAS

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    1. Harvey, Andrew & Koopman, Siem Jan & Riani, Marco, 1997. "The Modeling and Seasonal Adjustment of Weekly Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 354-368, July.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    3. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    4. Pierce, David A & Grupe, Michael R & Cleveland, William P, 1984. "Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 260-270, July.
    5. Harvey, Andrew & Scott, Andrew, 1994. "Seasonality in Dynamic Regression Models," Economic Journal, Royal Economic Society, vol. 104(427), pages 1324-1345, November.
    6. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
    7. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
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    Cited by:

    1. Prakash, Navendu & Srivastava, Bhavya & Singh, Shveta & Sharma, Seema & Jain, Sonali, 2022. "Effectiveness of social distancing interventions in containing COVID-19 incidence: International evidence using Kalman filter," Economics & Human Biology, Elsevier, vol. 44(C).
    2. James Rude & Yves Surry, 2014. "Canadian Hog Supply Response: A Provincial Level Analysis," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 62(2), pages 149-169, June.
    3. Dilaver, Zafer & Hunt, Lester C, 2011. "Modelling and forecasting Turkish residential electricity demand," Energy Policy, Elsevier, vol. 39(6), pages 3117-3127, June.
    4. Deb, Prokash & Dey, Madan M. & Surathkal, Prasanna, 2021. "Fish Price Volatility Dynamics in Bangladesh," 2021 Annual Meeting, August 1-3, Austin, Texas 314077, Agricultural and Applied Economics Association.
    5. Maria Jesus Herrerias and Eric Girardin, 2013. "Seasonal Patterns of Energy in China," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    6. A. Bers & Fernando Momo & Irene Schloss & Doris Abele, 2013. "Analysis of trends and sudden changes in long-term environmental data from King George Island (Antarctica): relationships between global climatic oscillations and local system response," Climatic Change, Springer, vol. 116(3), pages 789-803, February.
    7. Rude, James & An, Henry, 2015. "Explaining grain and oilseed price volatility: The role of export restrictions," Food Policy, Elsevier, vol. 57(C), pages 83-92.
    8. Danica Unevska-Andonova, 2018. "Inflation Decomposition Model: Application to Macedonian inflation," Working Papers 2018-06, National Bank of the Republic of North Macedonia.

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    More about this item

    Keywords

    SUTSE; cointegration; ARIMA; smoothing; likelihood;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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