Modelling of scale change, periodicity and conditional heteroskedasticity in return volatility

Yuanhua Feng*, Alexander J. McNeil

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper extends the GARCH model to a wide class of nonstationary processes by proposing a semiparametric GARCH model for simultaneous modelling of conditional heteroskedasticity, slow scale change and periodicity in the volatility of high-frequency financial returns. A data-driven algorithm is developed for estimating the model. An approximate significance test of daily periodicity and the use of Monte Carlo confidence bounds for the scale function are proposed. The practical performance of the proposal is investigated in detail using some German stock price returns. It is shown that the various volatility components are all significant. Asymptotic properties of the proposed estimators are investigated.

Original languageEnglish
Pages (from-to)850-867
Number of pages18
JournalEconomic Modelling
Issue number5
Publication statusPublished - Sept 2008


  • C14
  • C51
  • High-frequency financial data
  • Nonparametric regression
  • Periodicity in volatility
  • Scale change
  • Semiparametric GARCH model

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