Short-range Dependence Vs. Long-range Dependence
Long-range and short-range dependent processes are characterised by their autocovariance functions.
In short-range dependent processes, the coupling between values at different times decreases rapidly as the time difference increases.
- The sum of the autocorrelation function over all lags is finite.
- As the lag increases, the autocorrelation function of short-range dependent processes decays quickly.
In long-range processes, the correlations at longer time scales are more significant.
- The area under the autocorrelation function summed over all lags is infinite .
- The decay of the autocorrelation function is often assumed to have the specific functional form,
where ρ(k) is the autocorrelation function at a lag k, α is a parameter in the interval (0,1) and the ~ means asymptotically proportional to as k approaches infinity.
Read more about this topic: Long-tail Traffic
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