Diagnosing the trend and bootstrapping the forecasting intervals using a semiparametric ARMA

Dominik Schulz (), Yuanhua Feng (), Thomas Gries (), Marlon Fritz () and Sebastian Letmathe ()
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Dominik Schulz: Paderborn University
Yuanhua Feng: Paderborn University
Thomas Gries: Paderborn University
Marlon Fritz: Hochschule Darmstadt
Sebastian Letmathe: DekaBank

No 168, Working Papers CIE from Paderborn University, CIE Center for International Economics

Abstract: In this paper, an updated version of the R package smoots (smoothing time se- ries) is introduced, which now includes functionalities for testing the linearity of trend functions and the stationarity of time series, which follow an additive com- ponent model, graphically and for forecasting as well as backtesting data-driven Semi-ARMA models. At first, the ideas for these new methods are developed. Fur- thermore, the Semi-Log-GARCH and the Semi-Log-ACD models are summarized as important model variants. Subsequently, the package is applied to test the trend functions in the monthly temperature changes of the Northern Hemisphere and the US Log-GDP for linearity. Moreover, the stationarity of the daily DAX returns and the VIX closing prices is assessed. Employing the smoots package, point forecasts and respective forecasting intervals are obtained for a variety of tted Semi-ARMA models and backtests of these models are conducted. The forecasting quality of the Semi-ARMA is also compared to that of other methods.

Keywords: Asymptotics; linearity test; bootstrapping; interval forecasting; R (search for similar items in EconPapers)
JEL-codes: C14 C51 (search for similar items in EconPapers)
Pages: 33
Date: 2026-03
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