Birnbaum-Saunders autoregressive conditional range model applied to stock index data

This article proposes a new approach to the conditional autoregressive range (CARR) model using the Birnbaum-Saunders (BS) distribution. The model aims to develop volatility clustering, which incorporates extreme fluctuations, using a time-varying evolution of the range process called the BSCARR model. Furthermore, diagnosis analysis tools for diagnosis analysis were developed to evaluate the goodness of fit, such as residual analysis, global influence measures based on Cook's distance, and local influence analysis. For illustrative purposes, three real financial market indices are analyzed. A comparison with classical CARR models was also carried out in these examples. The results indicated that the proposed model outperformed some existing models in the literature, especially a recent CARR model based on the gamma distribution even under the presence of atypical cases (observed values).