Sums Of Exponentials Of Random Walks With Drift
For many time series in empirical macro and finance, it is assumed that the logarithm of the series is a unit root process. Since we may want to assume a stable growth rate for the macroeconomics time series, it seems natural to potentially model such a series as a unit root process with drift. This assumption implies that the level of such a time series is the exponential of a unit root process with drift and therefore, it is of substantial interest to investigate analytically the behavior of the exponential of a unit root process with drift. This paper shows that the sum of the exponential of a random walk with drift converges in distribution, after rescaling by the exponential of the maximum value of the random walk process. A similar result was established in earlier work for unit root processes without drift. The results derived here suggest the conjecture that also in the case when the Dickey-Fuller test or the KPSS statistic is applied to the exponential of a unit root process with drift, these tests will asymptotically indicate stationarity.
Volume (Year): 28 (2012)
Issue (Month): 04 (August)
|Contact details of provider:|| Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK|
Web page: http://journals.cambridge.org/jid_ECT
When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:28:y:2012:i:04:p:915-924_00. 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: (Keith Waters)
If references are entirely missing, you can add them using this form.