Dependence of increment in time series via large deviations

Analysis of increments dependence is an actual problem in testing of data series. The classic way is estimating the autocorrelation function of time series increments. This estimates are rather small and mutually independent in the case of independent increments, while it can be large in the case of dependent increments. But sequential values of the autocorrelation function are small and dependent in many cases. To prove dependence of increments, we repeat autocorrelation calculations: we calculate estimates for autocorrelation of autocorrelation function. Values of this twice-autocorrelation function are appeared to be rather large. That is, probabilities to have such values under the independence hypothesis are very small. We calculate it using a theorem on large deviations. We apply these results to text analysis: the better a text the lesser this probability.