# 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(TaiwanAirBox032017[1:100,1:3]), r.max = 1, type =2) ```

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