`Weak` trends for inference and forecasting in finite samples

Guillaume Chevillon

No 210, Economics Series Working Papers from University of Oxford, Department of Economics

Abstract: 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.

Keywords: Stochastic Trend; Deterministic Trend; Local Asymptotics; Multi-step Forecasting (search for similar items in EconPapers)
JEL-codes: C22 C52 C53 (search for similar items in EconPapers)
Date: 2004-12-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Working Paper: "Weak" trends for inference and forecasting in finite samples (2004)
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