Estimation of Lévy CARMA models in the yuima package: application on the financial time series

In this work we show how to use the R package yuima available on CRAN for the estimation of a Continuous Autoregressive Moving Average (CARMA) model on the real data. When dealing with the CARMA model, one of the advantages of the yuima package is the possibility of recovering the increments of the underlying noise and choosing the appropriate Lévy model. The estimation of the parameters for the underlying L´evy process makes yuima package appealing for modeling financial time series. Indeed, identifying the appropriate noise for a CARMA model allows to capture asymmetry and heavy tails observed in the real data.