Geodesic
The maximum likelihood method for Student's t-distributed autoregressive model with infinite variance
Mathematica Applicanda, Tome 48 (2020) no. 2, pp. 133-156.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Discrete-time series models are popular in different applications. The most classical one is the autoregressive moving average (ARMA) time series that is the stationary model. In its classical version, the ARMA model is based on Gaussian distribution. However, the gaussianity is a too simplistic assumption for many real phenomena description, especially when large observations may appear in the data. Thus, we are departing from the assumption of the normal distribution of the data and propose the infinite-variance AR model based on the Student's t-distribution. We introduce the maximum likelihood method for the estimation of the model's parameters. The idea is based on the Maclaurin series expansion of the likelihood function. The effectiveness of the proposed approach is demonstrated using Monte Carlo simulations. Finally, the real financial time series are considered by using the presented methodology.
DOI : 10.14708/ma.v48i2.7059
Classification : 92C50, 62P10
Mots-clés : autoregressive model, Student’s t-distribution, estimation, Monte Carlo simulations 
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Agnieszka Wyłomańska; Paweł Stępniak. The maximum likelihood method for Student's t-distributed autoregressive model with infinite variance. Mathematica Applicanda, Tome 48 (2020) no. 2, pp.  133-156. doi : 10.14708/ma.v48i2.7059. http://geodesic.mathdoc.fr/articles/10.14708/ma.v48i2.7059/

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