timedom {freqdom}

Defines a linear filter

Description

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

Usage

timedom(A, lags)

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.

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.

See Also

freqdom, is.timedom

Examples

# 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)