timedom: Defines a linear filter

Description

Creates an object of class timedom. This object corresponds to a multivariate linear filter.

Usage

timedom(A, lags)

Value

Returns an object of class timedom. An object of class timedom is a list containing the following components:

operators $\quad$ returns the array A as given in the argument.
lags $\quad$ returns the vector lags as given in the argument.

Arguments

A: a vector, matrix or array. If array, the elements $A[,,k], 1\leq k\leq K$, are real valued $(d_1\times d_2)$ matrices (all of same dimension). If A is a matrix, the $k$-th row is treated as $A[,,k]$. Same for the $k$-th element of a vector. These matrices, vectors or scalars define a linear filter.
lags: a vector of increasing integers. It corresponds to the time lags of the filter.

Details

This class is used to describe a linear filter, i.e. a sequence of matrices, each of which correspond to a certain lag. Filters can, for example, be used to transform a sequence $(X_t)$ into a new sequence $(Y_t)$ by defining $$ Y_t=\sum_k A_kX_{t-k}. $$ See filter.process(). Formally we consider a collection $[A_1,\ldots,A_K]$ of complex-valued matrices $A_k$, all of which have the same dimension $d_1\times d_2$. Moreover, we consider lags $\ell_1<\ell_2<\cdots<\ell_K$. The object this function creates corresponds to the mapping $f: \mathrm{lags}\to \mathbf{R}^{d_1\times d_2}$, where $\ell_k\mapsto A_k$.

Examples

Run this code

# In this example we apply the difference operator: Delta X_t= X_t-X_{t-1} to a time series
X = rar(20)
OP = array(0,c(2,2,2))
OP[,,1] = diag(2)
OP[,,2] = -diag(2)
A = timedom(OP, lags = c(0,1))
filter.process(X, A)