Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity – what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d = 1/2, and arrays of autoregressive process...
| Autors principals: | , |
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| Format: | Journal article |
| Idioma: | English |
| Publicat: |
Institute of Mathematical Statistics
2021
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| _version_ | 1826305865936797696 |
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| author | Duffy, J Kasparis, I |
| author_facet | Duffy, J Kasparis, I |
| author_sort | Duffy, J |
| collection | OXFORD |
| description | We provide new limit theory for functionals of a general class of
processes lying at the boundary between stationarity and nonstationarity – what we term weakly nonstationary processes (WNPs). This
includes, as leading examples, fractional processes with d = 1/2, and
arrays of autoregressive processes with roots drifting slowly towards
unity. We first apply the theory to study inference in parametric and
nonparametric regression models involving WNPs as covariates. We
then use these results to develop a new specification test for parametric regression models. By construction, our specification test statistic
has a χ
2
limiting distribution regardless of the form and extent of
persistence of the regressor, implying that a practitioner can validly
perform the test using a fixed critical value, while remaining agnostic
about the mechanism generating the regressor. Simulation exercises
confirm that the test controls size across a wide range of data generating processes, and outperforms a comparable test due to Wang
and Phillips (2012, Ann. Stat.) against many alternatives. |
| first_indexed | 2024-03-07T06:39:20Z |
| format | Journal article |
| id | oxford-uuid:f8bb6d7c-eb3e-4272-87e9-01888996bf69 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:39:20Z |
| publishDate | 2021 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:f8bb6d7c-eb3e-4272-87e9-01888996bf692022-03-27T12:52:38ZEstimation and inference in the presence of fractional d=1/2 and weakly nonstationary processesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f8bb6d7c-eb3e-4272-87e9-01888996bf69EnglishSymplectic ElementsInstitute of Mathematical Statistics2021Duffy, JKasparis, IWe provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity – what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional processes with d = 1/2, and arrays of autoregressive processes with roots drifting slowly towards unity. We first apply the theory to study inference in parametric and nonparametric regression models involving WNPs as covariates. We then use these results to develop a new specification test for parametric regression models. By construction, our specification test statistic has a χ 2 limiting distribution regardless of the form and extent of persistence of the regressor, implying that a practitioner can validly perform the test using a fixed critical value, while remaining agnostic about the mechanism generating the regressor. Simulation exercises confirm that the test controls size across a wide range of data generating processes, and outperforms a comparable test due to Wang and Phillips (2012, Ann. Stat.) against many alternatives. |
| spellingShingle | Duffy, J Kasparis, I Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title | Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title_full | Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title_fullStr | Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title_full_unstemmed | Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title_short | Estimation and inference in the presence of fractional d=1/2 and weakly nonstationary processes |
| title_sort | estimation and inference in the presence of fractional d 1 2 and weakly nonstationary processes |
| work_keys_str_mv | AT duffyj estimationandinferenceinthepresenceoffractionald12andweaklynonstationaryprocesses AT kasparisi estimationandinferenceinthepresenceoffractionald12andweaklynonstationaryprocesses |