moment.test

This function tests the existence of k-th moment by randomized method in
Trapani (2016).

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

moment.test function

<dl><dt>x</dt>
<dd>a numeric vector of data samples.</dd>
<dt>k</dt>
<dd>a number no smaller than 4, indicating that the procedure will test
the existence of the k-th moment when k is even. Otherwise, the procedure
will test the existence of the \(k'\)-th moment, with
\(k'=round(k/2,0)\times 2\).</dd>
<dt>R</dt>
<dd>the number of standard Gaussian variables generated in the
randomized test; see more details in Trapani (2016).</dd></dl>

Arguments

Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu

Author

test whether the k-th moment exists — moment.test

<dl>

<dt>x</dt>
<dd>a numeric vector of data samples.</dd>


<dt>k</dt>
<dd>a number no smaller than 4, indicating that the procedure will test
the existence of the k-th moment when k is even. Otherwise, the procedure
will test the existence of the \(k'\)-th moment, with
\(k'=round(k/2,0)\times 2\).</dd>


<dt>R</dt>
<dd>the number of standard Gaussian variables generated in the
randomized test; see more details in Trapani (2016).</dd>

</dl>

moment.test: test whether the k-th moment exists

Description

Usage

Value

Arguments

Author

Details

References

Examples