Is integration I(d) applicable to observed economics and finance time series?
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Joseph L. McCauley, 2008. "Time vs. Ensemble Averages for Nonstationary Time Series," Papers 0804.0902, arXiv.org.
- 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.
- David A. Dickey & Dennis W. Jansen & Daniel L. Thornton, 1991. "A primer on cointegration with an application to money and income," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 58-78.
- 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, 03.
- 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.
- Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-18.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:finana:v:18:y:2009:i:3:p:101-108. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.