## Improved methods for statistical inference in the context of various types of parameter variation

dc.contributor.advisor | Perron, Pierre | en_US |

dc.contributor.author | Casini, Alessandro | en_US |

dc.date.accessioned | 2019-12-12T18:32:38Z | |

dc.date.available | 2019-12-12T18:32:38Z | |

dc.date.issued | 2019 | |

dc.identifier.uri | https://hdl.handle.net/2144/38750 | |

dc.description.abstract | This dissertation addresses various issues related to statistical inference in the context of parameter time-variation. The problem is considered within general regression models as well as in the context of methods for forecast evaluation. The first chapter develops a theory of evolutionary spectra for heteroskedasticityand autocorrelation-robust (HAR) inference when the data may not satisfy secondorder stationarity. We introduce a class of nonstationary stochastic processes that have a time-varying spectral representation and presents a new positive semidefinite heteroskedasticity- and autocorrelation consistent (HAC) estimator. We obtain an optimal HAC estimator under the mean-squared error (MSE) criterion and show its consistency. We propose a data-dependent procedure based on a “plug-in” approach that determines the bandwidth parameters for given kernels and a given sample size. The second chapter develops a continuous record asymptotic framework to build inference methods for the date of a structural change in a linear regression model. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The third chapter develops a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. As the sampling interval between observations shrinks to zero the sequence of forecast losses is approximated by a continuous-time stochastic process possessing certain pathwise properties. We consider an hypotheses testing problem based on the local properties of the continuous-time limit counterpart of the sequence of losses. The fourth chapter develops a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes. The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. On the theoretical side, depending on some smoothing parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution of the least-squares estimator, or a Bayes-type asymptotic distribution. | en_US |

dc.language.iso | en_US | |

dc.subject | Economics | en_US |

dc.title | Improved methods for statistical inference in the context of various types of parameter variation | en_US |

dc.type | Thesis/Dissertation | en_US |

dc.date.updated | 2019-11-12T20:01:12Z | |

etd.degree.name | Doctor of Philosophy | en_US |

etd.degree.level | doctoral | en_US |

etd.degree.discipline | Economics | en_US |

etd.degree.grantor | Boston University | en_US |

dc.identifier.orcid | 0000-0002-1088-4802 |

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