This function determined the numbers of row and column factors
for matrix variate data under a two-way factor model, using a projected method.

We provide two algorithms for monitoring change points with online matrix-valued time series, under the assumption of a two-way factor structure. The algorithms are based on different calculations of the second moment matrices. One is based on stacking the columns of matrix observations, while another is by a more delicate projected approach. A well-known fact is that, in the presence of a change point, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a change point, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a change point. This package also provides some simple functions for detecting and removing outliers, imputing missing entries and testing moments. See more details in He et al. (2021)<arXiv:2112.13479>.

Long Yu

OLCPM

Online Change Point Detection for Matrix-Valued Time Series

Yong He

Xinbing Kong

Lorenzo Trapani

kpe function

<dl><dt>Y</dt>
<dd>data, a \(T\times p1\times p2\) array.</dd>
<dt>kmax</dt>
<dd>a positive integer smaller than p2, indicating the
upper bound for the factor numbers, and the dimension of projection matrix.</dd>
<dt>c</dt>
<dd>a non-negative but small number, to ensure the
denominator of the eigenvalue ratio statistics is not 0.</dd></dl>

Arguments

determine factor number - projected — kpe

<dl>

<dt>Y</dt>
<dd>data, a \(T\times p1\times p2\) array.</dd>


<dt>kmax</dt>
<dd>a positive integer smaller than p2, indicating the
upper bound for the factor numbers, and the dimension of projection matrix.</dd>


<dt>c</dt>
<dd>a non-negative but small number, to ensure the
denominator of the eigenvalue ratio statistics is not 0.</dd>

</dl>

kpe: determine factor number - projected

Description

Usage

Value

Arguments

References

Examples