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Is integration I(d) applicable to observed economics and finance time series?

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Listed:
  • McCauley, Joseph L.
  • Bassler, Kevin E.
  • Gunaratne, Gemunu H.

Abstract

The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called 'integration I(d)'. A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectations in standard economics. Detrended finance market returns are martingales, and martingales do not satisfy regression equations. We ask if there exist detrended processes beyond standard regression models that satisfy integration I(d). We show that stationary increment martingales are confined to the Wiener process, and observe that martingales describing finance data admit neither the integration I(d) nor the ergodicity required for long time equilibrium relationships. In particular, the martingales derived from finance data do not admit the time (or 'space') translational invariance required for increment stationarity. Our analysis explains the lack of equilibrium observed earlier between FX rates and relative price levels.

Suggested Citation

  • McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2009. "Is integration I(d) applicable to observed economics and finance time series?," International Review of Financial Analysis, Elsevier, vol. 18(3), pages 101-108, June.
    • Handle: RePEc:eee:finana:v:18:y:2009:i:3:p:101-108
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    References listed on IDEAS

    as
    1. Joseph L. McCauley, 2008. "Time vs. Ensemble Averages for Nonstationary Time Series," Papers 0804.0902, arXiv.org.
    2. Katarina Juselius & Ronald MacDonald, 2000. "International Parity Relationships between Germany and the United States: A Joint Modelling Approach," Discussion Papers 00-10, University of Copenhagen. Department of Economics.
    3. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2008. "Empirically based modeling in financial economics and beyond, and spurious stylized facts," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 767-783, December.
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    5. David A. Dickey & Dennis W. Jansen & Daniel L. Thornton, 1994. "A Primer on Cointegration with an Application to Money and Income," Palgrave Macmillan Books, in: B. Bhaskara Rao (ed.), Cointegration, chapter 2, pages 9-45, Palgrave Macmillan.
    6. Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, March.
    7. McCauley, Joseph L., 2008. "Nonstationarity of efficient finance markets: FX market evolution from stability to instability," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 820-837, December.
    8. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 14(Spr), pages 3-18.
    9. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, detrending data, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 202-216.
    10. McCauley, Joseph L., 2008. "Time vs. ensemble averages for nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5518-5522.
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