var.exp

This function calculates the cumulative explanatory power of the
leading row factors, in terms of the explained variance, under a
two-way factor structure.

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

var.exp function

<dl><dt>Y</dt>
<dd>data, a \(T\times p1\times p2\) array.</dd>
<dt>k</dt>
<dd>a positive integer indicating the number of factors investigated, should be
smaller than p1.</dd>
<dt>type</dt>
<dd>indicates how to calculate the sample covariance. "flat" for the
flat version, while others for the projected version.</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>plot</dt>
<dd>a logical value. When plot=1, a figure of the
cumulative explanatory power will be plotted, with x axis being the number of
factors, and y axis being the cumulative explained variance.</dd></dl>

Arguments

explanatory power of factors — var.exp

<dl>

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


<dt>k</dt>
<dd>a positive integer indicating the number of factors investigated, should be
smaller than p1.</dd>


<dt>type</dt>
<dd>indicates how to calculate the sample covariance. "flat" for the
flat version, while others for the projected version.</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>plot</dt>
<dd>a logical value. When plot=1, a figure of the
cumulative explanatory power will be plotted, with x axis being the number of
factors, and y axis being the cumulative explained variance.</dd>

</dl>

var.exp: explanatory power of factors

Description

Usage

Value

Arguments

Examples