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Testing for Stochastic Trends in Series with Structural Breaks

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  • Fabio Busetti

    (Banca d'Italia)

Abstract

This paper considers the problem of testing for the presence of stochastic trends in multivariate time series with structural breaks. The breakpoints are assumed to be known. The testing framework is the multivariate Locally Best Invariant test and the common trend test of Nyblom and Harvey (2000). The asymptotic distributions of the test statistics are derived under a general specification of the deterministic component, which allows for structural breaks as a particular case. Asymptotic critical values are provided for the case of a single breakpoint. A modified statistic is then proposed, the asymptotic distribution of which is independent of the breakpoint location and belongs to the Cram�r-von Mises family. This modification is particularly advantageous in the case of multiple breakpoints. It is also shown that the asymptotic distributions of the test statistics are unchanged when seasonal dummy variables and/or weakly dependent exogenous regressors are included. Finally, as an example, the tests are applied to UK macroeconomic data and to data on road casualties in Great Britain.

Suggested Citation

  • Fabio Busetti, 2000. "Testing for Stochastic Trends in Series with Structural Breaks," Temi di discussione (Economic working papers) 385, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_385_00
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    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2000/2000-0385/tema_385_00.pdf
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    Cited by:

    1. Luca Dedola & Eugenio Gaiotti & Luca Silipo, 2001. "Money demand in the euro area: do national differences matter?," Temi di discussione (Economic working papers) 405, Bank of Italy, Economic Research and International Relations Area.

    More about this item

    Keywords

    cointegration; common trends; Cram�r-von Mises distribution; locally best invariant test; structural breaks;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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