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Efficient Semiparametric Detection of Changes in Trend

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  • Chuan Goh

Abstract

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.

Suggested Citation

  • Chuan Goh, 2009. "Efficient Semiparametric Detection of Changes in Trend," Working Papers tecipa-373, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-373
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    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-373.pdf
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    References listed on IDEAS

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    1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, November.
    2. Donald W. K. Andrews & Marcia M. A. Schafgans, 1998. "Semiparametric Estimation of the Intercept of a Sample Selection Model," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 497-517.
    3. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, pages 265-283.
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    More about this item

    Keywords

    Structural change; trend-stationary processes; nonparametric regression; efficient influence function;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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