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Testing for trends in correlated data

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  • Sun, Hongguang
  • Pantula, Sastry G.
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    Abstract

    The problem of testing for the significance of a linear trend in the presence of positively correlated errors is considered. Test criteria based on ordinary least squares, conditional maximum likelihood, estimated generalized least squares and maximum likelihood estimates tend to have higher significance levels than nominal levels for positively correlated series of moderate length. In this paper, we study three alternative methods: (a) pre-test, (b) bias-adjusted, and (c) bootstrap-based procedures. A simulation study is used to compare the empirical level and power of different procedures. An example is used to illustrate the procedures.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 41 (1999)
    Issue (Month): 1 (January)
    Pages: 87-95

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    Handle: RePEc:eee:stapro:v:41:y:1999:i:1:p:87-95

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    Related research

    Keywords: Maximum likelihood Power Bootstrap;

    References

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    1. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    2. Charles R. Nelson & Heejoon Kang, 1983. "Pitfalls in the use of Time as an Explanatory Variable in Regression," NBER Technical Working Papers 0030, National Bureau of Economic Research, Inc.
    3. Park, Rolla Edward & Mitchell, Bridger M., 1980. "Estimating the autocorrelated error model with trended data," Journal of Econometrics, Elsevier, vol. 13(2), pages 185-201, June.
    4. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
    5. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
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    Cited by:
    1. Pierre Perron & Tomoyoshi Yabu, 2007. "Estimating Deterministic Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-020, Boston University - Department of Economics.
    2. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2006. "A simple, robust and powerful test of the trend hypothesis," Discussion Papers 06/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    3. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research and International Relations Area.
    4. Paul Newbold & Stephan Pfaffenzeller & Anthony Rayner, 2005. "How well are long-run commodity price series characterized by trend components?," Journal of International Development, John Wiley & Sons, Ltd., vol. 17(4), pages 479-494.

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