outliers.hdts: Multivariate Outlier Detection In SLBDD: Statistical Learning for Big Dependent Data

Description

Outlier detection in high dimensional time series by using projections as in Galeano, Peña and Tsay (2006).

Usage

 1 outliers.hdts(x, r.max, type)

Arguments

 x T by k data matrix: T data points in rows with each row being data at a given time point, and k time series in columns. r.max The maximum number of factors including stationary and non-stationary. type The type of series, i.e., 1 if stationary or 2 if nonstationary.

Value

A list containing:

• x.clean - The time series cleaned at the end of the procedure (n x m).

• P.clean - The estimate of the loading matrix if the number of factors is positive.

• Ft.clean - The estimated dynamic factors if the number of factors is positive.

• Nt.clean - The idiosyncratic residuals if the number of factors is positive.

• times.idi.out - The times of the idiosyncratic outliers.

• comps.idi.out - The components of the noise affected by the idiosyncratic outliers.

• sizes.idi.out - The sizes of the idiosyncratic outliers.

• stats.idi.out - The statistics of the idiosyncratic outliers.

• times.fac.out - The times of the factor outliers.

• comps.fac.out - The dynamic factors affected by the factor outliers.

• sizes.fac.out - The sizes of the factor outliers.

• stats.fac.out - The statistics of the factor outliers.

• x.kurt - The time series cleaned in the kurtosis sub-step (n x m).

• times.kurt - The outliers detected in the kurtosis sub-step.

• pro.kurt - The projection number of the detected outliers in the kurtosis sub-step.

• n.pro.kurt - The number of projections leading to outliers in the kurtosis sub-step.

• x.rand - The time series cleaned in the random projections sub-step (n x m).

• times.rand - The outliers detected in the random projections sub-step.

• x.uni - The time series cleaned after the univariate substep (n x m).

• times.uni - The vector of outliers detected with the univariate substep.

• comps.uni - The components affected by the outliers detected with the univariate substep.

• r.rob - The number of factors estimated (1 x 1).

• P.rob - The estimate of the loading matrix (m x r.rob).

• V.rob - The estimate of the orthonormal complement to P (m x (m - r.rob)).

• I.cov.rob - The matrix (V'GnV)^-1 used to compute the statistics to detect the idiosyncratic outliers.

• IC.1 - The values of the information criterion of Bai and Ng.

References

Galeano, P., Peña, D., and Tsay, R. S. (2006). Outlier detection in multivariate time series by projection pursuit. Journal of the American Statistical Association, 101(474), 654-669.

Examples

 1 2 data(TaiwanAirBox032017) output <- outliers.hdts(as.matrix(:100,1:3]), r.max = 1, type =2)

SLBDD documentation built on March 27, 2021, 9:07 a.m.