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

Davide Delle Monache (), Stefano Grassi () and Paolo Santucci ()

Studies in Economics from School of Economics, University of Kent

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.

Keywords: Long Memory; ARFIMA Processes; Level Shifts; State-Space methods; KPSS test (search for similar items in EconPapers)
JEL-codes: C10 C11 C22 C80 (search for similar items in EconPapers)
Date: 2015-07
New Economics Papers: this item is included in nep-ets and nep-ore
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