### Abstract

Original language | Undefined/Unknown |
---|---|

Pages (from-to) | 2725-2730 |

Number of pages | 6 |

Journal | Statistics & probability letters |

Volume | 78 |

Issue number | 16 |

Publication status | Published - 2008 |

### Cite this

*Statistics & probability letters*,

*78*(16), 2725-2730.

**The functional central limit theorem for a family of GARCH models.** / Berkes, István I.; Hörmann, Siegfried; Horvath, Lajos.

Research output: Contribution to journal › Article › Research › peer-review

*Statistics & probability letters*, vol. 78, no. 16, pp. 2725-2730.

}

TY - JOUR

T1 - The functional central limit theorem for a family of GARCH models

AU - Berkes, István I.

AU - Hörmann, Siegfried

AU - Horvath, Lajos

N1 - Language of publication: en

PY - 2008

Y1 - 2008

N2 - We consider polynomial GARCH(p,q) variables which define an important subclass of Duan's augmented GARCH(p,q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey--Fuller statistics under optimal conditions.

AB - We consider polynomial GARCH(p,q) variables which define an important subclass of Duan's augmented GARCH(p,q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey--Fuller statistics under optimal conditions.

M3 - Artikel

VL - 78

SP - 2725

EP - 2730

JO - Statistics & probability letters

JF - Statistics & probability letters

SN - 0167-7152

IS - 16

ER -