Sums of exponentials of random walks with drift
نویسندگان
چکیده
For many time series in empirical macro and finance, it is assumed that the logarithms of the series is a unit root processes. This assumption implies that the level of such a time series is the exponential of a unit root process. Therefore, it is of interest to investigate the behavior of such time series prior to taking their logarithms. 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.
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