Transformed GARMA model: Properties and simulations

Real time series can present anomalies, like non-additivity, non-normality, and heteroscedasticity, which makes using GARMA models impossible. Our article introduces a new class of models called Transformed Generalized Autoregressive Moving Average (TGARMA) models that allow using transformations to guarantee the GARMA assumptions. We present an extensive simulation study of the influence of the transformation on GARMA estimation. We also propose using bootstrap methods to get more information about the distribution of the transformation parameter. We apply the methodology to data related to annual Swedish fertility rates.