Efficient Semiparametric Detection of Changes in Trend
First
draft: 8 June 2008
This
version: 20 May 2009
Submitted for publication
Abstract
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This
paper proposes a test for the correct specification of a dynamic time-series model
that is taken to be stationary about a deterministic linear trend function
with no more than a finite number of discontinuities in the vector of trend
coefficients. The test avoids the
consideration of explicit alternatives to the null of trend stability. The proposal also does not involve the
detailed modelling of the data-generating process of the stochastic
component, which is simply assumed to satisfy a certain strong invariance
principle for stationary causal processes taking a general form. As such, the resulting inference procedure
is effectively an omnibus specification test for segmented linear trend
stationarity. The test is of
Wald-type, and is based on an asymptotically linear estimator of the vector
of total-variation norms of the trend parameters whose influence function
coincides with the efficient influence function. Simulations
illustrate the utility of this procedure to detect discrete breaks or
continuous variation in the trend parameter as well as alternatives where the
trend coefficients change randomly each period. This paper also includes an application
examining the adequacy of a linear trend-stationary specification with
infrequent trend breaks for the historical evolution of U.S. real output. |
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KEYWORDS: Structural change, trend-stationary
processes, nonparametric regression, efficient influence function |
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