The difference-sign runs length distribution in testing for serial independence

Abstract

We investigate the sequence of difference-sign runs length of a time series in the context of non-parametric tests for serial independence. This sequence is, under suitable conditioning, a stationary sequence and we prove that the normalized correlation of two consecutive runs length is small (≈0.0427).We use this result in a test based on the relative entropy of the empirical distribution of the runs length. We investigate the performance of the test in simulated series and test serial independence of cardiac data series in atrial fibrillation. © 2011 Taylor & Francis

A method to assess randomness of functional connectivity matrices

“…In fact, there are efficient random tests developed for vectors (Cammarota, 2011; Wald and Wolfowitz, 1940). One of the most widely used tests for vector randomness is the runs test (Bradley, 1960; Wald and Wolfowitz, 1940) which checks randomness for data sequences [x 1 x 2 x 3 …].…”

Estimating the turning point location in shifted exponential model of time series

“…Finally the serial independence should be also carefully investigated. Testing serial independence of residuals in cardiac series after detrending requires non parametric methods as the one considered in Cammarota [2011].…”

Detection of Hidden Attacks on Cyber-Physical Systems from Serial Magnitude and Sign Randomness Inconsistencies

“…Our recent works on attack detectors that monitor for nonrandom residual behavior have enabled the ability to find previously undetectable attacks when compared to conventional detection procedures. In [8], a windowed detector leveraging the Wilcoxon-Signed Rank [9] and Serial Independence Runs [10] tests was proposed to find non-random patterns over a sequence of sensor data. Similarly, in [11] we characterized the Cumulative Sign (CUSIGN) detector with the purpose arXiv:2104.15097v1 [eess.SY] 30 Apr 2021 of finding non-random signed residual behavior by checking for changes in probability of the signed values.…”

“…While a smart attacker may be able to fool the magnitude-based monitor as discussed in Section III-A, an attacker may leave traces of non-random behavior on the signed test measure difference. The test we use to monitor for signed randomness is influenced by the Serial Independence Runs (SIR) Test [10]. An example of the SIR test is shown in Fig.…”