### Abstract

Motivated by the need to describe regime switching in stock prices, we introduce and study a stochastic process in continuous time with two regimes and one threshold driving the change in regimes. When the difference between the regimes is simply given by different sets of real-valued parameters for the drift and diffusion coefficients, we show that there are consistent estimators for the threshold as long as we know how to classify a given observation of the process as belonging to one of the two regimes.

Original language | English |
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Title of host publication | Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies |

Editors | J. Lita da Silva, F. Caeiro, I. Natário, C. Braumann |

Place of Publication | Berlin, Heidelberg |

Publisher | Springer International Publishing Switzerland |

Pages | 297-305 |

Number of pages | 9 |

ISBN (Electronic) | 978-3-642-34904-1 |

ISBN (Print) | 978-3-642-34903-4 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

### Publication series

Name | Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies |
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Publisher | Springer International Publishing |

ISSN (Print) | 2194-7767 |

ISSN (Electronic) | 2194-7775 |

### Keywords

- Consistent estimator
- Single threshold
- Stochastic differential equation
- Stock prex
- Uhlenbeck process

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## Cite this

Mota, P. P. (2013). On a continuous-time stock price model with two mean reverting regimes. In J. Lita da Silva, F. Caeiro, I. Natário, & C. Braumann (Eds.),

*Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies*(pp. 297-305). (Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies). Berlin, Heidelberg: Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-642-34904-1_31