ctbi.outlier {ctbi}

ctbi.outlier

Description

Please cite the following companion paper if you're using the ctbi package: Ritter, F.: Technical note: A procedure to clean, decompose, and aggregate time series, Hydrol. Earth Syst. Sci., 27, 349–361, https://doi.org/10.5194/hess-27-349-2023, 2023.

Outliers in an univariate dataset y are flagged using an enhanced box plot rule (called Logbox, input: coeff.outlier) that is adapted to non-Gaussian data and keeps the type I error at \frac{0.1}{\sqrt{n}} % (percentage of erroneously flagged outliers).

The box plot rule flags data points as outliers if they are below L or above U using the sample quantile q:

L = q(0.25)-\alpha \times (q(0.75)- q(0.25))

U = q(0.75)+\alpha \times (q(0.75)- q(0.25))

Logbox replaces the original \alpha = 1.5 constant of the box plot rule with \alpha = A \times \log(n)+B+\frac{C}{n}. The variable n \geq 9 is the sample size, C = 36 corrects biases emerging in small samples, and A and B are automatically calculated on a predictor of the maximum tail weight defined as m_{*} = \max(m_{-},m_{+})-0.6165.

The two functions (m_{-},m_{+}) are defined as:

m_{-} = \frac{q(0.875)- q(0.625)}{q(0.75)- q(0.25)}

m_{+} = \frac{q(0.375)- q(0.125)}{q(0.75)- q(0.25)}

And finally, A = f_{A}(m_{*}) and B = f_{B}(m_{*}) with m_{*} restricted to [0,2]. The functions (f_{A},f_{B}) are defined as:

f_{A}(x) = 0.2294\exp(2.9416x-0.0512x^{2}-0.0684x^{3})

f_{B}(x) = 1.0585+15.6960x-17.3618x^{2}+28.3511x^{3}-11.4726x^{4}

Both functions have been calibrated on the Generalized Extreme Value and Pearson families.

Usage

ctbi.outlier(y, coeff.outlier = "auto")

Arguments

y

univariate data (numeric vector)

coeff.outlier

one of coeff.outlier = 'auto' (default value), coeff.outlier = 'gaussian', coeff.outlier = c(A,B,C) or coeff.outlier = NA. If coeff.outlier = 'auto', C = 36 and the coefficients A and B are calculated on m_{*}. If coeff.outlier = 'gaussian', coeff.outlier = c(0.08,2,36), adapted to the Gaussian distribution. If coeff.outlier = NA, no outliers are flagged

Value

A list that contains:

xy, a two columns data frame that contains the clean data (first column) and the outliers (second column)

summary.outlier, a vector that contains A, B, C, m_{*}, the size of the residuals (n), and the lower and upper outlier threshold

Examples

x <- runif(30)
x[c(5,10,20)] <- c(-10,15,30)
example1 <- ctbi.outlier(x)