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**Processes with volatility-induced stationarity: An application for interest rates.**
*(English)*
Zbl 1130.60072

Summary: 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.

### MSC:

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

91G30 | Interest rates, asset pricing, etc. (stochastic models) |

### Keywords:

stochastic differential equations; diffusion processes; parametric estimation; non-parametric estimation
Full Text:
DOI

### References:

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