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26 Initially, denote the sample √ in order of increasing magnitude again as x1 x2 . . xn . 229). Please note, that for sufficient large n, which is assumed for the test, C must be positive. Hence, it is required that 1 α> √ . 2n − 1 This means that at least n > 220 observations were required for a 5%, and n > 5, 100 for a 1% significance level. The test hypotheses of the r smallest observations to be outliers in Walsh’s outlier test are: Hmin : The r smallest values are members of Fn−r 0 vs. 224).

Note, that the popular variant to sample not in transaction but in calendar time and to estimate RV(5,Y) , which “5” indicating to sample once every five minutes, will reduce the microstructure noise caused bias but at the cost of missing to use most of the data. This procedure is also known as sparse sampling. But, sampling once each five minutes instead of once a second will reduce the sample size by factor 300. Sampling every transaction possibly even more. 1 on page 20. It is hence recommendable to use all available data and to model the noise, even if the noise distribution is misspecified, see Aït-Sahalia et al.

G. sequences of zeros, but can not account for errors masked through a trend in the time series. 2b, accounts for time dependencies using a ±3σ error bound (with σ the standard deviation) and identifies those observations as outliers, that are not within the error boundaries. The Grubbs test Grubbs’ test for outlier detection tests for the significance of the largest (respectively the smallest) observation in a normal distributed sample of size n. Denote the sample in order of increasing magnitude as x1 x2 ...