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Testing for trends in correlated data

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  • Sun, Hongguang
  • Pantula, Sastry G.

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.

Suggested Citation

  • Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:1:p:87-95
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    References listed on IDEAS

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    4. Consuelo Arellano & Sastry G. Pantula, 1995. "Testing For Trend Stationarity Versus Difference Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 147-164, March.
    5. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    6. 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.
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    Cited by:

    1. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 1302-1330, December.
    2. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    3. Jiawen Xu & Pierre Perron, 2013. "Robust testing of time trend and mean with unknown integration order errors Frequency (and Other) Contaminations," Boston University - Department of Economics - Working Papers Series 2013-006, Boston University - Department of Economics.
    4. Teresa Alpuim & Abdel El-Shaarawi, 2008. "On the efficiency of regression analysis with AR(p) errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 717-737.
    5. Busetti, Fabio & Harvey, Andrew, 2008. "Testing For Trend," Econometric Theory, Cambridge University Press, vol. 24(1), pages 72-87, February.
    6. 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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    Keywords

    Maximum likelihood Power Bootstrap;

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