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Testing for Level Shifts in Fractionally Integrated Processes: a State Space Approach

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  • Davide Delle Monache
  • Stefano Grassi
  • Paolo Santucci

Abstract

Short memory models contaminated by level shifts have similar long-memory features as fractionally integrated processes. This makes hard to verify whether the true data generating process is a pure fractionally integrated process when employing standard estimation methods based on the autocorrelation function or the periodogram. In this paper, we propose a robust testing procedure, based on an encompassing parametric specification that allows to disentangle the level shifts from the fractionally integrated component. The estimation is carried out on the basis of a state-space methodology and it leads to a robust estimate of the fractional integration parameter also in presence of level shifts. Once the memory parameter is correctly estimated, we use the KPSS test for presence of level shift. The Monte Carlo simulations show how this approach produces unbiased estimates of the memory parameter when shifts in the mean, or other slowly varying trends, are present in the data. Therefore, the subsequent robust version of the KPSS test for the presence of level shifts has proper size and by far the highest power compared to other existing tests. Finally, we illustrate the usefulness of the proposed approach on financial data, such as daily bipower variation and turnover.

Suggested Citation

  • Davide Delle Monache & Stefano Grassi & Paolo Santucci, 2015. "Testing for Level Shifts in Fractionally Integrated Processes: a State Space Approach," Studies in Economics 1511, School of Economics, University of Kent.
  • Handle: RePEc:ukc:ukcedp:1511
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    More about this item

    Keywords

    Long Memory; ARFIMA Processes; Level Shifts; State-Space methods; KPSS test;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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