Dual-trend and dual long-memory time series modelling

Shujie Li () and Yuanhua Feng ()
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Shujie Li: Paderborn University
Yuanhua Feng: Paderborn University

No 174, Working Papers CIE from Paderborn University, CIE Center for International Economics

Abstract: Many economic and financial series exhibit non-stationarity as well as long-memory behavior in both the first and second moments. To capture both non-stationarity and long-memory characteristics simultaneously, a general dual-trend and dual longmemory framework is proposed. In this framework, the error term of the semiparametric FARIMA model is assumed to exhibit a slowly changing scale and longmemory heteroskedasticity. A four-step estimation procedure is proposed, including a trend and a FARIMA model estimation for the first moment, followed by a scaling function and a long-memory volatility model estimation for the second moment. Three long-memory EGARCH-type models and the FIGARCH model are employed in the final stage. Our results indicate that the proposed approach can effectively model the selected economic series exhibiting dual-trend and dual long-memory features.

Keywords: dual-trend; dual long-memory; semi-strong FARIMA; modulus FILog- GARCH; modified FIEGARCH; FIEGARCH and FIGARCH (search for similar items in EconPapers)
JEL-codes: C14 C22 C58 (search for similar items in EconPapers)
Pages: 29
Date: 2026-03
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