ccid (version 1.2.0)

preaverage: Preaveraging the multivariate time series

Description

This function pre-processes the given data in order to remove serial correlation that might exist in the given data.

Usage

preaverage(X, scal = 3)

Arguments

X

A numerical matrix representing the multivariate time series, with the columns representing its components.

scal

A positive integer number with default value equal to 3. It is used to define the way we pre-average the data sequences.

Value

The ``preaveraged'' matrix \(\tilde{X}\) of dimensionality \(Q \times d\), as explained in Details.

Details

For a given natural number scal and data matrix X of dimensionality \(T \times d\), let us denote by \(Q = \lceil T/scal \rceil\). Then, preaverage calculates, for all \(j = 1,2, ..., d\), $$\tilde{X}_{q, j} = 1/scal\sum_{t=(q-1) * sc + 1}^{q * sc}X_{t, j},$$ for \(q=1, 2, ..., Q-1\), while $$\tilde{x}_{Q, j} = (T - (Q-1) * sc)^{-1}\sum_{t = (Q-1) * sc + 1}^{T}X_{t, j}.$$

References

``Cross-covariance isolate detect: a new change-point method for estimating dynamic functional connectivity'', Anastasiou et al (2020), preprint <doi:10.1101/2020.12.20.423696>.

Examples

# NOT RUN {
A <- matrix(1:32, 8, 4)
A
A1 <- preaverage(A, scal = 3)
A1
# }