Yield Curve Modelling Using a Multivariate Higher-Order HMM
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.
KeywordsInterest Rate Root Mean Square Error Hide Markov Model Absolute Percentage Error Hide Markov Model Model
- 13.Guidolin, M., Timmermann, A.:Forecasts of US short-term interest rates: A flexible forecast combination approach. Journal of Econometrics. 150: 297–311 (2009).Google Scholar
- 18.Nieh, C-C., Wu, S., Zeng, Y.: Regime shifts and the term structure of interest rates. In: Lee, C-F., Lee, J.: Handbook of Quantitative Finance and Risk Management, pp.1121–1134, Springer, (2010).Google Scholar
- 21.Cajueiro, D.O., Tabak, B.M.: Time-varying long-range dependence in US interest rates. Chaos, Solitons & Fractals. 34, 360–367 (2007).Google Scholar
- 23.Maheu, J.: Can GARCH models capture long-range dependence? Studies in Nonlinear Dynamics. 9, Article 1 (2005).Google Scholar
- 26.Solberg, J.: Modelling Random Processes for Engineers and Managers. Wiley & Sons, Inc., New Jersey (2009).Google Scholar