outlier_detection {mlmts}

Constructs the outlier detection procedure of López-Oriona and Vilar (2021)

Description

outlier_detection computes the outlier detection method for MTS proposed by Lopez-Oriona and Vilar (2021).

Usage

outlier_detection(X, levels = c(0.1, 0.5, 0.9), alpha = NULL)

Arguments

X

A list of MTS (numerical matrices).

levels

The set of probability levels to compute the QCD-estimates.

alpha

The desired rate of outliers to detect (a real number between 0 and 1).

Details

This function performs outlier detection according to the procedure proposed by Lopez-Oriona and Vilar (2021). Specifically, each MTS in the original set is described by means of a multivariate functional datum by using an estimate of its quantile cross- spectral density. Given the corresponding set of multivariate functional data, the functional depth of each object is computed. Based on depth computations, the outlying elements are the objects with low values for the depths.

Value

A list with two elements:

• Depths. The functional depths associated with elements in X, sorted in increasing order.

• Indexes. The corresponding indexes associated with the vector Depths.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Lopez-Oriona A, Vilar JA (2021). “Outlier detection for multivariate time series: A functional data approach.” Knowledge-Based Systems, 233, 107527.

See Also

dis_qcd

Examples

outliers <- outlier_detection(SyntheticData2$data[c(1 : 3, 65)])
outliers$Indexes[1] # The first outlying MTS in dataset SyntheticData2
outliers$Depths[1] # The corresponding value for the depths