Modelling Seasonal Volatility and Level Shift in Fractionally Integrated Processes

Authors

  • Lawrence Dhliwayo Department of Statistics, University of Zimbabwe, Harare, Zimbabwe.
  • Florance Matarise Department of Statistics, University of Zimbabwe, Harare, Zimbabwe.
  • Charles Chimedza School of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South Africa.

DOI:

https://doi.org/10.9734/bpi/rhmcs/v2/2967C

Keywords:

Seasonality, fractional integration, long-memory, level shift, SLS-SARFIMA, SLS-GARCH, volatility

Abstract

This chapter introduces a class of seasonal fractionally integrated autoregressive moving average-generalized conditional heteroscedasticity (SARFIMAGARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modelling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models was derived. Test statistics that are useful to examine if seasonal level shift in an SARFIMA-GARCH model is statistically plausible were introduced. Estimation of SLS-SARFIMA and SLS-GARCH parameters are also given.

Published

2022-10-31

How to Cite

Lawrence Dhliwayo, Florance Matarise, & Charles Chimedza. (2022). Modelling Seasonal Volatility and Level Shift in Fractionally Integrated Processes . Research Highlights in Mathematics and Computer Science Vol. 2, 116–142. https://doi.org/10.9734/bpi/rhmcs/v2/2967C

Issue

Research Highlights in Mathematics and Computer Science Vol. 2

Section

Chapters