Combining Long Memory and Level Shifts in Modelling and Forecasting the Volatility of Asset Returns

Rasmus T. Varneskov, Pierre Perron

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.
Original languageEnglish
JournalQuantitative Finance
Volume18
Issue number3
Pages (from-to)371-393
Number of pages23
ISSN1469-7688
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • Forecasting
  • Kalman filter
  • Long memory processes
  • State space modelling
  • Stochastic volatility
  • Structural change

Cite this

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title = "Combining Long Memory and Level Shifts in Modelling and Forecasting the Volatility of Asset Returns",
abstract = "We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10{\%} Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.",
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Combining Long Memory and Level Shifts in Modelling and Forecasting the Volatility of Asset Returns. / Varneskov, Rasmus T.; Perron, Pierre.

In: Quantitative Finance, Vol. 18, No. 3, 2018, p. 371-393.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Combining Long Memory and Level Shifts in Modelling and Forecasting the Volatility of Asset Returns

AU - Varneskov, Rasmus T.

AU - Perron, Pierre

PY - 2018

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N2 - We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.

AB - We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.

KW - Forecasting

KW - Kalman filter

KW - Long memory processes

KW - State space modelling

KW - Stochastic volatility

KW - Structural change

KW - Forecasting

KW - Kalman filter

KW - Long memory processes

KW - State space modelling

KW - Stochastic volatility

KW - Structural change

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