IDEAS home Printed from https://ideas.repec.org/p/uto/dipeco/201401.html

Modelli strutturali e Filtri di Kalman per serie storiche univariate. Teoria ed applicazioni con Gretl

Author

Listed:

Abstract

Il Filtro di Kalman è una tecnica statistica per fare previsioni e stimare parametri in opportuni modelli per serie storiche. Questi modelli sono i modelli strutturali nello Spazio degli Stati, così detti perchè con essi il dato storico è strutturato linearmente in componenti non osservabili, la cui variazione di stato (nel tempo) è regolata da equazioni lineari. Formalmente il Filtro di Kalman è un predittore lineare che fornisce previsioni ottimali del processo stocastico allo studio; è un previsore particolare, perchè si costruice come un palazzo: un piano (stato temporale) alla volta. Sembra una tecnica complessa perchè utilizza formule apparentemente complesse, ma, se non ci si spaventa difronte a qualche “formulaccia”, ci si accorge che è una tecnica abbastanza duttile ed utile in molti contesti. Proprio per non spaventare e demotivare lo studente, questa dispensa è stata pensata nel seguente modo: un primo capitolo in cui sono illustrate i punti salienti della metodologia cercando nel possibile di limitare le “formulacce”!) e quattro successivi capitoli dedicati ognuno ad un caso studio. L'intento è quello di llustrare la tecnica in maniera pratica, attraverso delle applicazioni che lo studente è invitato a replicare. Anche per questo, è stata dedicata un'appendice all'uso del Filtro di Kalman in Gretl, il software con il quale sono state realizzate le applicazioni nei casi studio.

Suggested Citation

  • Chirico, Paolo, 2014. "Modelli strutturali e Filtri di Kalman per serie storiche univariate. Teoria ed applicazioni con Gretl," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201401, University of Turin.
    • Handle: RePEc:uto:dipeco:201401
    as

    Download full text from publisher

    File URL: http://www.est.unito.it/do/home.pl/Download?doc=/allegati/wp2014dip/wp_1_2014.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    2. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    3. Lucchetti, Riccardo, 2011. "State Space Methods in gretl," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 41(i11).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state–space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
    2. Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    3. Strickland, Chris M. & Martin, Gael M. & Forbes, Catherine S., 2008. "Parameterisation and efficient MCMC estimation of non-Gaussian state space models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2911-2930, February.
    4. Ben Tims & Ronald Mahieu, 2006. "A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 409-424.
    5. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    6. repec:spo:wpmain:info:hdl:2441/1461 is not listed on IDEAS
    7. Shanker, Latha, 2017. "New indices of adequate and excess speculation and their relationship with volatility in the crude oil futures market," Journal of Commodity Markets, Elsevier, vol. 5(C), pages 18-35.
    8. Andres, P. & Harvey, A., 2012. "The Dyanamic Location/Scale Model: with applications to intra-day financial data," Cambridge Working Papers in Economics 1240, Faculty of Economics, University of Cambridge.
    9. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    10. Hang Qian, 2014. "A Flexible State Space Model And Its Applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 79-88, March.
    11. Rodríguez, Alejandro & Ruiz, Esther, 2012. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 62-74, January.
    12. George Kapetanios & Elias Tzavalis, 2006. "Stochastic Volatility Driven by Large Shocks," Working Papers 568, Queen Mary University of London, School of Economics and Finance.
    13. Michel Beine & Charles S. Bos & Sébastien Laurent, 2007. "The Impact of Central Bank FX Interventions on Currency Components," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 154-183.
    14. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    15. repec:tin:wpaper:20230016 is not listed on IDEAS
    16. Neil Shephard, 2013. "Martingale unobserved component models," Economics Papers 2013-W01, Economics Group, Nuffield College, University of Oxford.
    17. Dieter Wang & Julia Schaumburg, 2020. "Smooth marginalized particle filters for dynamic network effect models," Tinbergen Institute Discussion Papers 20-023/III, Tinbergen Institute.
    18. Roberto Leon‐Gonzalez & Blessings Majoni, 2025. "Exact likelihood for inverse gamma stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 46(4), pages 774-795, July.
    19. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.
    20. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    21. Matteo Pelagatti & Giacomo Sbrana, 2020. "Estimating high dimensional multivariate stochastic volatility models," Working Papers 428, University of Milano-Bicocca, Department of Economics, revised Jan 2020.
    22. Caldeira, João F & Moura, Guilherme Valle & Santos, André Alves Portela, 2013. "Seleção de carteiras utilizando o modelo Fama-French-Carhart," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 67(1), April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uto:dipeco:201401. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Laura Ballestra or Cinzia Carlevaris (email available below). General contact details of provider: https://edirc.repec.org/data/detorit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.