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Testing for trend

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Author Info
Fabio Busetti () (Bank of Italy)
Andrew Harvey () (Cambridge University)

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Abstract

The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope as well as against a purely deterministic slope. The test may be modified, parametrically or nonparametrically to deal with serial correlation. Using both local limiting power arguments and finite sample Monte Carlo results, we compare the t-test with the nonparametric tests of Vogelsang (1998) and with a modified stationarity test. Overall the t-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data. When standardized by the square root of the sample size, the simple t-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic. We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope. Empirical illustrations are provided using series of relative prices in the euro-area and data on global temperature.

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Paper provided by Bank of Italy, Economic Research Department in its series Temi di discussione (Economic working papers) with number 614.

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Date of creation: Feb 2007
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Handle: RePEc:bdi:wptemi:td_614_07

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Web page: http://www.bancaditalia.it
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Related research
Keywords: Cramér-von Mises distribution stationarity test stochastic trend unit root unobserved component.

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Luca Dedola & Sylvain Leduc, 2001. "Why Is the Business-Cycle Behavior of Fundamentals Alike Across Exchange-Rate Regimes?," Working Papers 53, Oesterreichische Nationalbank (Austrian Central Bank). [Downloadable!]
    Other versions:
  2. Lippi, F., 1999. "Median Voter Preferences, Central Bank Independence and Conservatis," Papers 351, Banca Italia - Servizio di Studi.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Mario Quagliariello, 2007. "Macroeconomic uncertainty and banks' lending decisions: The case of Italy," Temi di discussione (Economic working papers) 615, Bank of Italy, Economic Research Department. [Downloadable!]
    Other versions:
  2. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School. [Downloadable!]
  3. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2006. "Inflation convergence and divergence within the European Monetary Union," Working Paper Series 574, European Central Bank. [Downloadable!]
    Other versions:
  4. James H. Stock & Mark W. Watson, 1996. "Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model," NBER Technical Working Papers 0201, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Massimiliano Affinito & Matteo Piazza, 2008. "What are borders made of? An analysis of barriers to European banking integration," Temi di discussione (Economic working papers) 666, Bank of Italy, Economic Research Department. [Downloadable!]
  6. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation, Yale University. [Downloadable!]
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