### 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 |
---|---|

Publisher | Springer International Publishing |

ISSN (Print) | 2194-7767 |

ISSN (Electronic) | 2194-7775 |

### Fingerprint

### Keywords

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

### Cite this

*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

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

**On a continuous-time stock price model with two mean reverting regimes.** / Mota, Pedro P.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - On a continuous-time stock price model with two mean reverting regimes

AU - Mota, Pedro P.

N1 - This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through PEst-OE/MAT/UI0297/2011 (CMA).

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - Consistent estimator

KW - Single threshold

KW - Stochastic differential equation

KW - Stock prex

KW - Uhlenbeck process

UR - http://www.scopus.com/inward/record.url?scp=85060281972&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-34904-1_31

DO - 10.1007/978-3-642-34904-1_31

M3 - Chapter

SN - 978-3-642-34903-4

T3 - Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies

SP - 297

EP - 305

BT - Studies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies

A2 - Lita da Silva, J.

A2 - Caeiro, F.

A2 - Natário, I.

A2 - Braumann, C.

PB - Springer International Publishing Switzerland

CY - Berlin, Heidelberg

ER -