Yield Curve Modelling Using a Multivariate Higher-Order HMM

  • Xiaojing Xi
  • Rogemar MamonEmail author
Part of the Statistics and Econometrics for Finance book series (SEFF, volume 1)


We develop a multivariate higher-order Markov model, also known as weak hidden Markov model (WHMM) for the term structure of interest rates. The means and volatilities of bond yields are governed by a second-order Markov chain in discrete time. WHMM enriches the usual HMM by incorporating more information from the past thereby capturing presence of memory in the underlying market state. The multivariate filtering technique in conjunction with the expectation–maximization algorithm are adopted to develop the optimal estimates of model parameters. We assess the goodness of fit of the one-step-ahead forecasts and apply the Akaike information criterion (AIC) in determining the optimal number of economic regimes. In this study, filtering algorithms were implemented to a dataset consisting of approximately 3 years of daily US-Treasury yields. Our empirical results show that based on the AIC and root-mean-square error metrics, a two-state WHMM is deemed the most appropriate in describing the term structure dynamics within the dataset and period considered. Moreover, an analysis of the h-day ahead predictions generated from WHMM is compared to those generated from the regular HMM. By including memories in the model, the WHMM outperforms the HMM in terms of low forecasting errors.


Interest Rate Root Mean Square Error Hide Markov Model Absolute Percentage Error Hide Markov Model Model 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsWestern UniversityLondonCanada
  2. 2.Department of Statistical and Actuarial SciencesWestern UniversityLondonCanada

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