Computational Economics

, Volume 44, Issue 3, pp 307–337

Capturing the Regime-Switching and Memory Properties of Interest Rates


  • Xiaojing Xi
    • Department of Applied MathematicsUniversity of Western Ontario
    • Department of Applied MathematicsUniversity of Western Ontario
    • Department of Statistical and Actuarial SciencesUniversity of Western Ontario

DOI: 10.1007/s10614-013-9396-5

Cite this article as:
Xi, X. & Mamon, R. Comput Econ (2014) 44: 307. doi:10.1007/s10614-013-9396-5


We propose a mean-reverting interest rate model whose mean-reverting level, speed of mean-reversion and volatility are all modulated by a weak Markov chain (WMC). This model features a simple way to capture the regime-switching evolution of the parameters as well as the memory property of the data. Concentrating on the second-order WMC framework, we derive the filters of the WMC and other auxiliary processes through a change of reference probability measure. Optimal estimates of model parameters are provided by employing the EM algorithm. The \(h\)-step ahead forecasts under our proposed set-up are examined and compared with those under the usual Markovian regime-switching framework. We obtain better goodness-of-fit performance based on our numerical results generated from the implementation of WMC-based filters to a 10-year dataset of weekly short-term-maturity Canadian yield rates. Some statistical inference issues of the proposed modelling approach are also discussed.


Weak hidden Markov modelParameter estimationRegime-switchingMemory property

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© Springer Science+Business Media New York 2013