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Efficient two-stage estimation of cyclical ARCH models

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  • Aknouche, Abdelhakim
  • Bentarzi, Mohamed

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.

Suggested Citation

  • Aknouche, Abdelhakim & Bentarzi, Mohamed, 2025. "Efficient two-stage estimation of cyclical ARCH models," MPRA Paper 127417, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:127417
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    References listed on IDEAS

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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