On model fitting and estimation of strictly stationary processes

Stationary processes have been extensively studied in the literature. Their applications include modelling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are considered, modelling is traditionally based on fitting an autoregressive moving average (ARMA) process. However, we challenge this conventional approach. Instead of fitting an ARMA model, we apply an AR$(1)$ characterization in modelling any strictly stationary processes. Moreover, we derive consistent and asymptotically normal estimators of the corresponding model parameter.