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

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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.

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  • 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
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    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).
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