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Stationarity Tests For Irregularly Spaced Observations And The Effects Of Sampling Frequency On Power


  • Busetti, Fabio
  • Taylor, A.M. Robert


In this paper, starting from continuous-time local level unobserved components models for stock and flow data we derive locally best invariant (LBI) stationarity tests for data available at potentially irregularly spaced points in time. We demonstrate that the form of the LBI test differs between stock and flow variables. In cases where the data are observed at regular intervals throughout the sample we show that the LBI tests for stock and flow data both reduce to the form of the standard stationarity test in the discrete-time local level model. Here we also show that the asymptotic local power of the LBI test increases with the sampling frequency in the case of stock, but not flow, variables. Moreover, for a fixed time span we show that the LBI test for stock (flow) variables is (is not) consistent against a fixed alternative as the sampling frequency increases to infinity. We also consider the case of mixed frequency data in some detail, providing asymptotic critical values for the LBI tests for both stock and flow variables, together with a finite sample power study. Our results suggest that tests which ignore the infra-period aspect of the data involve rather small losses in efficiency relative to the LBI test in the case of flow variables, but can result in significant losses of efficiency when analysing stock variables.
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Suggested Citation

  • Busetti, Fabio & Taylor, A.M. Robert, 2005. "Stationarity Tests For Irregularly Spaced Observations And The Effects Of Sampling Frequency On Power," Econometric Theory, Cambridge University Press, vol. 21(04), pages 757-794, August.
  • Handle: RePEc:cup:etheor:v:21:y:2005:i:04:p:757-794_05

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    Cited by:

    1. J. Isaac Miller & Xi Wang, 2016. "Implementing Residual-Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 810-824, November.
    2. J. Isaac Miller, 2018. "Testing Cointegrating Relationships Using Irregular and Non-Contemporaneous Series with an Application to Paleoclimate Data," Working Papers 1809, Department of Economics, University of Missouri.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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