LG_spectrum_norm: Compute norms, distances and angles between different spectra

In LAJordanger/localgaussSpec: Local Gaussian Spectral Analysis

Compute norms, distances and angles between different spectra

Description

This internal function can compute norms of the spectra (seen as members of a Hilbert space), and it can also compute the distances and angles between different spectra.

Usage

LG_spectrum_norm(C1_env = NULL, W1 = NULL, C2_env = NULL, W2 = NULL)

Arguments

C1_env	The environment containing the coefficients used for the first collection of spectra. These coefficients will be scaled with the weights from W1. Reminder: A copy of the look_up-argument must be added to this environment before this function is called!
W1	A vector with the weights to be used for the scaling of the coefficients given in C1_env, i.e. the scaling that truncates the estimates at a given lag. It will always be assumed that W1 is symmetric around the lag zero component, so only the positive lags are specified. It is furthermore only necessary to specify the nonzero weights, so this vector can thus be shorter than the one given in C1_env. If this argument is left unspecified, i.e. if the default value NULL is given, then it will be assumed that all the weights should be 1.
C2_env	An optional environment that can be used when it is of interest to compute the distance between two families of spectra (i.e. the spectra based on coefficients and weights in C1_env and W1, and the spectra based on C2_env and W2). The default value for C2_env is NULL. Note that the structure of the content of this environment does not need to be identical to the one in C1_env, since the comparison will be based on the common components. Reminder: If the target of interest is the distance of the spectra from white noise, then it is sufficient to 'take the square root of norm minus one' in the auto-correlation case. For the cross-spectra it is sufficient to simply take the square root of the norm. Reminder: A copy of the look_up-argument must be added to this environment before this function is called!
W2	An optional vector with the weights to be used for the scaling of the coefficients given in C2_env. The same assumptions occur for W2 as those specified for W1.

Value

The result of this function is an environment with a collection of norms, distances and angles related to the investigated spectra. If both C1_env and C2_env are given, then the following four variations will be returned: C1-local vs. C1-global, C2-local vs. C2-global, C1-global vs. C2-global, and C1-local vs. C2-local.

LAJordanger/localgaussSpec documentation built on May 6, 2023, 4:31 a.m.