Long memory of financial time series and hidden Markov models with time-varying parameters

Peter Nystrup, Henrik Madsen, Erik Lindström

Research output: Contribution to conferencePaperResearchpeer-review

Abstract

Hidden Markov models are often used to capture stylized facts of daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior for the ability to reproduce the stylized facts have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time-varying. It is shown that a two-state Gaussian hidden Markov model with time-varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step predictions.
Original languageEnglish
Publication date2015
Number of pages23
Publication statusPublished - 2015
Event22nd International Forecasting Financial Markets Conference - Rennes, France
Duration: 20 May 201522 May 2015

Conference

Conference22nd International Forecasting Financial Markets Conference
CountryFrance
CityRennes
Period20/05/201522/05/2015

Keywords

  • Hidden Markov models
  • Daily returns
  • Stylized facts
  • Long memory
  • Time-varying parameters
  • Leptokurtosis

Cite this

Nystrup, P., Madsen, H., & Lindström, E. (2015). Long memory of financial time series and hidden Markov models with time-varying parameters. Paper presented at 22nd International Forecasting Financial Markets Conference, Rennes, France.
Nystrup, Peter ; Madsen, Henrik ; Lindström, Erik. / Long memory of financial time series and hidden Markov models with time-varying parameters. Paper presented at 22nd International Forecasting Financial Markets Conference, Rennes, France.23 p.
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author = "Peter Nystrup and Henrik Madsen and Erik Lindstr{\"o}m",
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Nystrup, P, Madsen, H & Lindström, E 2015, 'Long memory of financial time series and hidden Markov models with time-varying parameters' Paper presented at 22nd International Forecasting Financial Markets Conference, Rennes, France, 20/05/2015 - 22/05/2015, .

Long memory of financial time series and hidden Markov models with time-varying parameters. / Nystrup, Peter; Madsen, Henrik; Lindström, Erik.

2015. Paper presented at 22nd International Forecasting Financial Markets Conference, Rennes, France.

Research output: Contribution to conferencePaperResearchpeer-review

TY - CONF

T1 - Long memory of financial time series and hidden Markov models with time-varying parameters

AU - Nystrup, Peter

AU - Madsen, Henrik

AU - Lindström, Erik

PY - 2015

Y1 - 2015

N2 - Hidden Markov models are often used to capture stylized facts of daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior for the ability to reproduce the stylized facts have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time-varying. It is shown that a two-state Gaussian hidden Markov model with time-varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step predictions.

AB - Hidden Markov models are often used to capture stylized facts of daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time-varying behavior for the ability to reproduce the stylized facts have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time-varying. It is shown that a two-state Gaussian hidden Markov model with time-varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time-varying behavior of the parameters also leads to improved one-step predictions.

KW - Hidden Markov models

KW - Daily returns

KW - Stylized facts

KW - Long memory

KW - Time-varying parameters

KW - Leptokurtosis

M3 - Paper

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Nystrup P, Madsen H, Lindström E. Long memory of financial time series and hidden Markov models with time-varying parameters. 2015. Paper presented at 22nd International Forecasting Financial Markets Conference, Rennes, France.