Long Memory of Financial Time Series and Hidden Markov Models with Time-Varying Parameters

Research output: Contribution to journalArticle


Hidden Markov models are often used to model 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 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 density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations.


External organisations
  • Technical University of Denmark
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics


  • Adaptive estimation, Daily returns, Hidden Markov models, Long memory, Time-varying parameters
Original languageEnglish
Pages (from-to)989-1002
JournalJournal of Forecasting
Issue number8
Early online date2016 Sep 13
Publication statusPublished - 2017 Dec
Publication categoryResearch