IDetect (version 0.1.0)

normalise: Transform the noise to be closer to the Gaussian distribution

Description

This function pre-processes the given data in order to obtain a noise structure that is closer to satisfying the Gaussianity assumption. See details for more information and for the relevant literature reference.

Usage

normalise(x, sc = 3)

Arguments

x

A numeric vector containing the data.

sc

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

Value

The ``normalised'' vector \(\tilde{x}\) of length \(Q\), as explained in Details.

Details

For a given natural number sc and data x of length \(T\), let us denote by \(Q = \lceil T/sc \rceil\). Then, normalise calculates $$\tilde{x}_q = 1/sc\sum_{t=(q-1) * sc + 1}^{q * sc}x_t,$$ for \(q=1, 2, ..., Q-1\), while $$\tilde{x}_Q = (T - (Q-1) * sc)^{-1}\sum_{t = (Q-1) * sc + 1}^{T}x_t.$$ More details can be found in the preprint ``Detecting multiple generalized change-points by isolating single ones'', Anastasiou and Fryzlewicz (2018).

See Also

ht_ID_pcm and ht_ID_cplm, which are functions that employ normalise.

Examples

# NOT RUN {
t5 <- rt(n = 10000, df = 5)
n5 <- normalise(t5, sc = 3)
# }