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Processes with volatility‐induced stationarity: an application for interest rates

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  • João Nicolau

Abstract

In this paper we propose a refinement of the existing definition of volatility‐induced stationarity that allows us to distinguish between processes with drift and diffusion induced stationarity and processes with pure volatility‐induced stationarity. We also propose a classification of stationary processes with volatility‐induced stationarity according to the volatility that is needed to inject stationarity. Processes with volatility‐induced stationarity are potentially applicable to interest rate time‐series since, as has been acknowledged, mean‐reversion effects occur mainly in periods of high volatility. As such, we provide evidence that the logarithm of the Fed funds rate can be modelled as a local martingale with volatility‐induced stationarity.

Suggested Citation

  • João Nicolau, 2005. "Processes with volatility‐induced stationarity: an application for interest rates," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(4), pages 376-396, November.
    • Handle: RePEc:bla:stanee:v:59:y:2005:i:4:p:376-396
    DOI: 10.1111/j.1467-9574.2005.00292.x
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    Cited by:

    1. Kanaya, Shin, 2017. "Convergence Rates Of Sums Of Α-Mixing Triangular Arrays: With An Application To Nonparametric Drift Function Estimation Of Continuous-Time Processes," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1121-1153, October.
    2. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    3. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    4. Anne Lundgaard Hansen, 2018. "Volatility-Induced Stationarity and Error-Correction in Macro-Finance Term Structure Modeling," Discussion Papers 18-12, University of Copenhagen. Department of Economics.
    5. Hansen, Anne Lundgaard, 2021. "Modeling persistent interest rates with double-autoregressive processes," Journal of Banking & Finance, Elsevier, vol. 133(C).
    6. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.

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