Summability of stochastic processes—a generalization of integration for non-linear processes
The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S(δ): (i) generalizes I(δ)...
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| Format: | Conference item |
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Elsevier
2013
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| _version_ | 1797103625343860736 |
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| author | Berenguer-Rico, V Gonzalo, J |
| author_facet | Berenguer-Rico, V Gonzalo, J |
| author_sort | Berenguer-Rico, V |
| collection | OXFORD |
| description | The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S(δ): (i) generalizes I(δ); (ii) measures the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of non-linear relationships; (iv) opens the door to the concept of co-summability which represents a generalization of co-integration for non-linear processes. To make this concept empirically applicable, an estimator for δ and its asymptotic properties are provided. The finite sample performance of subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with the estimation of the degree of summability of the macroeconomic variables in an extended version of the Nelson-Plosser database. |
| first_indexed | 2024-03-07T06:22:43Z |
| format | Conference item |
| id | oxford-uuid:f338a033-4681-43c6-9294-7dfc049035d9 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:22:43Z |
| publishDate | 2013 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:f338a033-4681-43c6-9294-7dfc049035d92022-03-27T12:10:29ZSummability of stochastic processes—a generalization of integration for non-linear processesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:f338a033-4681-43c6-9294-7dfc049035d9Symplectic Elements at OxfordElsevier2013Berenguer-Rico, VGonzalo, JThe order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) to handle non-linearities. The paper shows that this new concept, S(δ): (i) generalizes I(δ); (ii) measures the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of non-linear relationships; (iv) opens the door to the concept of co-summability which represents a generalization of co-integration for non-linear processes. To make this concept empirically applicable, an estimator for δ and its asymptotic properties are provided. The finite sample performance of subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with the estimation of the degree of summability of the macroeconomic variables in an extended version of the Nelson-Plosser database. |
| spellingShingle | Berenguer-Rico, V Gonzalo, J Summability of stochastic processes—a generalization of integration for non-linear processes |
| title | Summability of stochastic processes—a generalization of integration for non-linear processes |
| title_full | Summability of stochastic processes—a generalization of integration for non-linear processes |
| title_fullStr | Summability of stochastic processes—a generalization of integration for non-linear processes |
| title_full_unstemmed | Summability of stochastic processes—a generalization of integration for non-linear processes |
| title_short | Summability of stochastic processes—a generalization of integration for non-linear processes |
| title_sort | summability of stochastic processes a generalization of integration for non linear processes |
| work_keys_str_mv | AT berenguerricov summabilityofstochasticprocessesageneralizationofintegrationfornonlinearprocesses AT gonzaloj summabilityofstochasticprocessesageneralizationofintegrationfornonlinearprocesses |