Efficient two-stage estimation of cyclical ARCH models

Aknouche, Abdelhakim and Bentarzi, Mohamed (2025): Efficient two-stage estimation of cyclical ARCH models.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Periodic ARCH, recursive online estimation, two-stage weighted least squares, two-stage recursive least squares, asymptotic normality.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General

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