Weak' trends for inference and forecasting in finite samples
This paper studies the small sample properties of processes which exhibit both a stochastic and a deterministic trend. Whereas for estimation, inference and forecasting purposes the latter asymptotically dominates the former, it is not so when only a finite number of observations is available and la...
| Autore principale: | |
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| Natura: | Working paper |
| Pubblicazione: |
University of Oxford
2004
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| _version_ | 1826283388915417088 |
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| author | Chevillon, G |
| author_facet | Chevillon, G |
| author_sort | Chevillon, G |
| collection | OXFORD |
| description | This paper studies the small sample properties of processes which exhibit both a stochastic and a deterministic trend. Whereas for estimation, inference and forecasting purposes the latter asymptotically dominates the former, it is not so when only a finite number of observations is available and large non-linearities in the parameters of the process result. To analyze this dependence, we resort to local-asymptotics and present the concept of a 'weak' trend whose coefficient is of order O(T-1/2), so that the deterministic trend is O(T1/2) and the process Op(T1/2). In this framework, parameter estimates, unit-root test statistics and forecast errors are functions of 'drifting' Ornstein-Uhlenbeck processes. We derive a comparison of direct and iterated multi-step estimation and forecasting of a - potentially misspecified - random walk with drift, and show that we explain well the non-linearities exhibited in finite samples. Another main benefit of direct multi-step estimation stems from some different behaviors of the 'multi-step' unit-root and slope tests under the weak and strong (constant coefficient) trend frameworks which could lead to testing which framework is more relevant. A Monte Carlo analysis validates the local-asymptotics approximation to the distributions of finite sample biases and test statistics. |
| first_indexed | 2024-03-07T00:58:10Z |
| format | Working paper |
| id | oxford-uuid:88cd6c12-754f-41d0-923c-a84222cc898a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:58:10Z |
| publishDate | 2004 |
| publisher | University of Oxford |
| record_format | dspace |
| spelling | oxford-uuid:88cd6c12-754f-41d0-923c-a84222cc898a2022-03-26T22:19:54ZWeak' trends for inference and forecasting in finite samplesWorking paperhttp://purl.org/coar/resource_type/c_8042uuid:88cd6c12-754f-41d0-923c-a84222cc898aBulk import via SwordSymplectic ElementsUniversity of Oxford2004Chevillon, GThis paper studies the small sample properties of processes which exhibit both a stochastic and a deterministic trend. Whereas for estimation, inference and forecasting purposes the latter asymptotically dominates the former, it is not so when only a finite number of observations is available and large non-linearities in the parameters of the process result. To analyze this dependence, we resort to local-asymptotics and present the concept of a 'weak' trend whose coefficient is of order O(T-1/2), so that the deterministic trend is O(T1/2) and the process Op(T1/2). In this framework, parameter estimates, unit-root test statistics and forecast errors are functions of 'drifting' Ornstein-Uhlenbeck processes. We derive a comparison of direct and iterated multi-step estimation and forecasting of a - potentially misspecified - random walk with drift, and show that we explain well the non-linearities exhibited in finite samples. Another main benefit of direct multi-step estimation stems from some different behaviors of the 'multi-step' unit-root and slope tests under the weak and strong (constant coefficient) trend frameworks which could lead to testing which framework is more relevant. A Monte Carlo analysis validates the local-asymptotics approximation to the distributions of finite sample biases and test statistics. |
| spellingShingle | Chevillon, G Weak' trends for inference and forecasting in finite samples |
| title | Weak' trends for inference and forecasting in finite samples |
| title_full | Weak' trends for inference and forecasting in finite samples |
| title_fullStr | Weak' trends for inference and forecasting in finite samples |
| title_full_unstemmed | Weak' trends for inference and forecasting in finite samples |
| title_short | Weak' trends for inference and forecasting in finite samples |
| title_sort | weak trends for inference and forecasting in finite samples |
| work_keys_str_mv | AT chevillong weaktrendsforinferenceandforecastinginfinitesamples |