inst/ctre-app/stabilityPlot.md

In CTRE: Thresholding Bursty Time Series

Stability Plots for Interarrival Times

Asymptotically (for high enough thresholds), the interarrival times (i.e. times between threshold crossings) follow a Mittag-Leffler distribution. The slider now chooses the maximum number of exceedances (the minimum height of the threshold). The estimates of the tail and (rescaled) scale parameters of the Mittag-Leffler distribution are plotted as the threshold varies from the minimum height to the 10th largest data point. To the left (high threshold), data are scarce and variance is high; to the right (low threshold), the asymptotics are off and bias is high. A region of 'stability' in the middle is choisen for a parameter estimate.

1. Adjust the Tail parameter to your choice of estimate
2. Then read off estimates of the scale parameter.

For instance, tail=0.85 and scale=3000 (days) seem to be a good fit for the Bitcoin trade dataset. This means that if the threshold is set to the k-th largest magnitude, then the interarrival times are Mittag-Leffler distributed with parameters tail = 0.85 and scale = 3000 / k^(1/tail).

CTRE documentation built on May 2, 2019, 9:34 a.m.