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 returns the array A as given in the argument.
lags 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 $Y_{t} = \sum_{k} A_{k} X_{t - k} .$ See filter.process(). Formally we consider a collection $[A_{1}, \dots, A_{K}]$ of complex-valued matrices $A_{k}$ , all of which have the same dimension $d_{1} \times d_{2}$ . Moreover, we consider lags $ℓ_{1} < ℓ_{2} < \dots < ℓ_{K}$ . The object this function creates corresponds to the mapping $f : lags \to R^{d_{1} \times d_{2}}$ , where $ℓ_{k} \mapsto A_{k}$ .

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)

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