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Fractionally Integrated Models with ARCH Errors: With an Application to the Swiss One-Month Euromarket Interest Rate

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  • Hauser, Michael A
  • Kunst, Robert M

Abstract

We introduce ARFIMA-ARCH models, which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and we use it to construct the bias-corrected maximum (modified profile) likelihood estimator. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. Backus and Zin (1993) have motivated the existence of fractional integration in interest rates by the persistence of the short rate and the variability of the long end of the yield curve. An empirical investigation of a daily one-month Swiss Euromarket interest rate finds a difference parameter of 0.72. This indicates non-stationary behavior. In contrast to first-order integrated models, the long-run cumulative response of shocks to the series is zero. Copyright 1998 by Kluwer Academic Publishers

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  • Hauser, Michael A & Kunst, Robert M, 1998. "Fractionally Integrated Models with ARCH Errors: With an Application to the Swiss One-Month Euromarket Interest Rate," Review of Quantitative Finance and Accounting, Springer, vol. 10(1), pages 95-113, January.
    • Handle: RePEc:kap:rqfnac:v:10:y:1998:i:1:p:95-113
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    Cited by:

    1. Gil-Alana, Luis A. & Gupta, Rangan, 2014. "Persistence and cycles in historical oil price data," Energy Economics, Elsevier, vol. 45(C), pages 511-516.
    2. Basma Bekdache & Christopher F. Baum, 1999. "A re-evaluation of empirical tests of the Fisher hypothesis," Computing in Economics and Finance 1999 944, Society for Computational Economics, revised 18 Sep 2000.
    3. Andreas Brunhart, 2014. "Stock Market's Reactions to Revelation of Tax Evasion: An Empirical Assessment," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 150(III), pages 161-190, September.
    4. Stavros Degiannakis, 2008. "ARFIMAX and ARFIMAX-TARCH realized volatility modeling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1169-1180.
    5. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.
    6. Emma Iglesias & Garry Phillips, 2005. "Analysing one-month Euro-market interest rates by fractionally integrated models," Applied Financial Economics, Taylor & Francis Journals, vol. 15(2), pages 95-106.
    7. Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.
    8. Margaret R. Maier & Nigel Meade, 2003. "Evidence of long memory in short-term interest rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(8), pages 553-568.

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