Levy sections theorem revisited

This paper revisits Levy sections theorem, which generalizes the central limit theorem to encompass autocorrelated variables. Levy sections theorem’s approach is extended to time series and applied to historical daily returns of selected dollar exchange rates. We explain the elevated kurtosis usually observed in such series by their volatilities. In particular, the high kurtosis of emerging markets’ exchange rates is explained by the duration of exchange rate pegs. Thus we suggest an alternative rationale for fat tails that is simpler than those based on either autocorrelations or the presence of Levy distributions. PACS: 89.65.Gh; 89.75.-k.