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Modeling volatility using state space models

J Timmer1, A S Weigend

  • 1Fakultät für Physik, Universität Freiburg, Germany. jeti@fdm.uni-freiburg.de

International Journal of Neural Systems
|August 1, 1997
PubMed
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Empirical volatilities contain significant observational noise. State space models accurately capture volatility dynamics, unlike autoregressive models that underestimate relaxation times.

Area of Science:

  • Quantitative Finance
  • Econometrics
  • Statistical Modeling

Background:

  • Time series analysis often faces challenges with noise, categorized as dynamic or observational.
  • Empirical volatilities, derived from squared relative price returns, are shown to contain substantial observational noise.
  • Existing models may not adequately differentiate between noise types, impacting accuracy.

Purpose of the Study:

  • To develop and apply state space models that explicitly account for observational noise in volatility.
  • To accurately model and predict the time evolution of empirical volatilities.
  • To compare the performance of these models against traditional autoregressive approaches.

Main Methods:

  • Estimation of state space models incorporating observational noise.

Related Experiment Videos

  • Analysis of high-frequency financial data, including foreign exchange rates and stock indices.
  • Comparison of relaxation times derived from state space models versus autoregressive models.

    • Main Results:

    • Empirical volatilities exhibit significant observational noise.
    • State space models reveal relaxation times for log volatility shocks from three weeks to five months.
    • A two-dimensional hidden state is often necessary for model residuals to approximate white noise.
    • Autoregressive models significantly underestimate relaxation times due to noise misclassification.

    Conclusions:

    • State space models provide a more accurate representation of volatility dynamics by distinguishing observational and dynamic noise.
    • This framework enhances understanding of financial time series, with implications for risk management and derivative pricing.
    • The concept of 'relaxators' in state space models offers a novel interpretation applicable to stochastic volatility and GARCH models.