An Extended Exponential SEMIFAR Model with Application in R

The article at hand provides a detailed description of the esemifar R-package, which is an extension of the already published smoots R-package, enabling the data-driven local-polynomial smoothing of trend-stationary time series with long memory. In this regard, a simple data-driven algorithm is proposed based on the well-known iterative plug-in algorithm for SEMIFAR (semiparametric fractional autoregressive) models. Two new functions for data-driven estimation of the trend and its derivatives in the presence of long memory are introduced. esemifar is applied to various environmental and financial time series with long memory, for example, mean monthly Northern Hemisphere temperature changes, daily observations of the air quality index of London (Britain), quarterly G7-GDP and daily trading volume of the S & P500. It is worth mentioning that this package can be applied to any suitable time series.