Outlier detection in high dimensional time series by using projections as in Galeano, Pe<U+00F1>a and Tsay (2006).
outliers.hdts(x, r.max, type)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.
The maximum number of factors including stationary and non-stationary.
The type of series, i.e., 1 if stationary or 2 if nonstationary.
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.
Galeano, P., Pe<U+00F1>a, 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.
# NOT RUN {
data(TaiwanAirBox032017)
output <- outliers.hdts(as.matrix(TaiwanAirBox032017[1:100,1:3]), r.max = 1, type =2)
# }
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