# wnorm: Calculate Weighted Norm of series In Rssa: A Collection of Methods for Singular Spectrum Analysis

## Description

Function calculates the W-norm for input objects or for objects stored in input ssa obect.

## Usage

 1 2 3 4 5 6 7 8 9 10 11 12 ## S3 method for class '1d.ssa' wnorm(x, ...) ## S3 method for class 'nd.ssa' wnorm(x, ...) ## S3 method for class 'toeplitz.ssa' wnorm(x, ...) ## S3 method for class 'mssa' wnorm(x, ...) ## Default S3 method: wnorm(x, L = (N + 1) %/% 2, ...) ## S3 method for class 'complex' wnorm(x, L = (N + 1) %/% 2, ...)

## Arguments

 x the input object. This might be ssa object for ssa method, or just a series. L window length. ... arguments to be passed to methods.

## Details

L-weighted norm of series is Frobenius norm of its L-trajectory matrix. So, if x is vector (series), the result of wnorm(x, L) is equal to sqrt(sum(hankel(x, L)^2), but in fact is calculated much more efficiently. For 1d SSA and Toeplitz SSA wnorm(x) calculates weighted norm for stored original input series and stored window length.

L-weighted norm of 2d array is Frobenius norm of its L[1] * L[2]-trajectory hankel-block-hankel matrix. For 2d SSA this method calculates weighted norm for stored original input array and stored 2d-window lengths.

## References

Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall/CRC. ISBN 1584881941