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International Conference on Time Series and Forecasting

ITISE 2021: Theory and Applications of Time Series Analysis and Forecasting pp 31–46Cite as

Unit Root Test Combination via Random Forests

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Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.

Keywords

  • ARIMA time series
  • Conditional inference trees
  • Monte Carlo simulation
  • Sequential testing
  • Supervised machine learning

The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Deutsche Bundesbank or the European Central Bank. The authors thank Uwe Hassler, Mehdi Hosseinkouchack and participants of the 2020 Conference on Machine Learning of Dynamic Processes and Time Series Analysis and of the 2021 International Conference on Time Series and Forecasting for valuable comments.

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Notes

  1. 1.

    To accommodate weaker assumptions about the errors, the KPSS test requires a consistent long-variance estimator rather than a variance estimator.

  2. 2.

    In our case, yi is binary (k = 1). However, k = 3 could also be used if we considered the combination of possibilities of having seasonal and non-seasonal unit roots.

  3. 3.

    Alternatively, though less conservative, we can condition only on those predictors \(\mathbf {{x}}^C_j\) whose correlation with xj exceeds a certain threshold.

  4. 4.

    For computational reasons and parsimony, the tests have been performed with minimal lag length. Seasonal differences and the seasonal status of the series are not considered. The finite-sample critical values that we obtained from our own simulations in R (version 3.5.1) are very similar to the ones tabulated in the original papers (details are available upon request).

  5. 5.

    Similar results are obtained for a nominal 5% significance level.

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Author information

Authors and Affiliations

  1. European Central Bank, Frankfurt, Germany

    Luca Nocciola

  2. Deutsche Bundesbank, Frankfurt, Germany

    Daniel Ollech & Karsten Webel

Authors
  1. Luca Nocciola
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  2. Daniel Ollech
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  3. Karsten Webel
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Corresponding author

Correspondence to Luca Nocciola .

Editor information

Editors and Affiliations

  1. Faculty of Sciences, University of Granada, Granada, Spain

    Olga Valenzuela

  2. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Fernando Rojas

  3. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Luis Javier Herrera

  4. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

  5. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

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Nocciola, L., Ollech, D., Webel, K. (2023). Unit Root Test Combination via Random Forests. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_3

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