Sums of exponentials of random walks with drift (Q2909253)

Motivated by some econometric applications (e.g., macroeconomic time series), this paper deals with the exponential of a random walk process with a drift, that is a unit root process with a drift. More precisely, the authors study the asymptotic behavior of the sum of such exponentials. The main result concerns the convergence in distribution of this sum under some assumption and is presented in Section 2, followed by the conjecture that this convergence result also holds for linear processes; hence the Dickey-Fuller test and the KPSS statistic applied to that case imply asymptotic stationarity. In Section 3, some simulations using \texttt{Fortran 90} are presented. Finally, the mathematical proofs of the main results are given in the Appendix.