The present work proposes a new class of model for random variables with support in the positive real line, this model explains the conditional quantile and is an alternative for modeling data that indicate asymmetric behavior and heavy tails. We present a new autoregressive moving average model based on the τ–th quantile of the Burr XII distribution (BXII-ARMA) since the quantile is less sensitive than the average of heterogeneous populations and also suitable in the presence of outliers. This model makes it possible to model any quantile by a dynamic structure containing autoregressive terms and moving averages, time-varying regressors, unknown parameters, and a link function. The conditional maximum likelihood method is considered to estimate the parameters and build the confidence intervals of the BXII-ARMA model. In addition, the model is adjusted to real data related to the financial market and compared with other competing models.
Tópico:
Statistical Distribution Estimation and Applications