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Testing for Neglected Nonlinearity in Long Memory Models

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Abstract

Interest in the interface of nonstationarity and nonlinearity has been increasing in the econometric literature. The motivation for this development maybe be traced to the perceived possibility that processes following nonlinear models maybe mistakenly taken to be unit root or long-memory nonstationary. This paper considers the possibility that processes may exhibit both long memory and nonlinearity. We test against the possibility that the process u t in the model (1-L) d y t = u t is nonlinear. We do not assume a particular parametric form for the nonlinear process but construct a pure significance test. Clearly, such a test could be straightforwardly constructed if d were known. Unfortunately, if a linear model is assumed while estimating d the power of the test will be reduced. We propose new more powerful tests for this problem. We present Monte Carlo evidence on the performance of the new tests and apply them to Yen real exchange rates.

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  • George Kapetanios, 2002. "Testing for Neglected Nonlinearity in Long Memory Models," Working Papers 473, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp473
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp473.pdf
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    1. repec:nsr:niesrd:153 is not listed on IDEAS
    2. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    3. Kapetanios, G., 1999. "Threshold Models for Trended Time Series," Cambridge Working Papers in Economics 9905, Faculty of Economics, University of Cambridge.
    4. Davidson, James & Sibbertsen, Philipp, 2005. "Generating schemes for long memory processes: regimes, aggregation and linearity," Journal of Econometrics, Elsevier, vol. 128(2), pages 253-282, October.
    5. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
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    Cited by:

    1. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    2. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(4), pages 693-724.
    3. Aaron Smallwood, 2004. "Joint Tests for Long Memory and Non-linearity: The Case of Purchasing Power Parity," Computing in Economics and Finance 2004 23, Society for Computational Economics.
    4. Smallwood, Aaron D., 2008. "Measuring the persistence of deviations from purchasing power parity with a fractionally integrated STAR model," Journal of International Money and Finance, Elsevier, vol. 27(7), pages 1161-1176, November.
    5. Richard T. Baillie & George Kapetanios, 2006. "Nonlinear Models with Strongly Dependent Processes and Applications to Forward Premia and Real Exchange Rates," Working Papers 570, Queen Mary University of London, School of Economics and Finance.
    6. Ulrike Busch & Dieter Nautz, 2010. "Controllability and Persistence of Money Market Rates along the Yield Curve: Evidence from the Euro Area," German Economic Review, Verein für Socialpolitik, vol. 11, pages 367-380, August.
    7. Kuswanto, Heri & Sibbertsen, Philipp, 2009. "Testing for Long Memory Against ESTAR Nonlinearities," Hannover Economic Papers (HEP) dp-427, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    8. Smallwood Aaron D, 2005. "Joint Tests for Non-linearity and Long Memory: The Case of Purchasing Power Parity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-30, June.
    9. Richard T. Baille & Claudio Morana, 2009. "Investigating Inflation Dynamics and Structural Change with an Adaptive ARFIMA Approach," ICER Working Papers - Applied Mathematics Series 06-2009, ICER - International Centre for Economic Research.
    10. ERIC HILLEBRAND & MArcelo Cunha Medeiros, 2010. "Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility," Textos para discussão 578, Department of Economics PUC-Rio (Brazil).

    More about this item

    Keywords

    Long memory; Nonlinearity; Neural networks; Real exchange rates.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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