Efficient two-stage estimation of cyclical ARCH models

Abdelhakim Aknouche and Mohamed Bentarzi

MPRA Paper from University Library of Munich, Germany

Abstract: Two estimation algorithms for Periodic Autoregressive Conditionally Heteroskedastic (PARCH ) models are developed in this work. The first is the two-stage weighted least squares (2S-WLS) algorithm, which adapts the ordinary least squares method for use in the periodic ARCH framework. The second, 2S-RLS, is an adaptation of the former for recursive online estimation contexts. Both algorithms produce consistent and asymptotically normally distributed estimators. Furthermore, the second method is particularly well-suited to capturing the dynamic characteristics of financial time series that are increasingly being observed at high frequencies. It also enables effective monitoring of positivity and periodic stationarity constraints.

Keywords: Periodic ARCH; recursive online estimation; two-stage weighted least squares; two-stage recursive least squares; asymptotic normality. (search for similar items in EconPapers)
JEL-codes: C10 C13 (search for similar items in EconPapers)
Date: 2025-12-20
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