preaverage {ccid} R Documentation

## 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.

### 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∑_{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}∑_{t = (Q-1) * sc + 1}^{T}X_{t, j}.

### Value

The “preaveraged” matrix \tilde{X} of dimensionality Q \times d, as explained in Details.

### Author(s)

Andreas Anastasiou, anastasiou.andreas@ucy.ac.cy

### 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

A <- matrix(1:32, 8, 4)
A
A1 <- preaverage(A, scal = 3)
A1


[Package ccid version 1.0.0 Index]