mfilter: Linear Filtering on a Multivariate Time Series

Description

Applies linear filtering to a multivariate time series.

Usage

mfilter(x, filter, method=c("convolution","recursive"), init)

Arguments

a multivariate ($m$-dimensional, $n$ length) time series $x[n,m]$.

filter

an array of filter coefficients. filter[i,j,k] shows the value of $i$-th row, $j$-th column, $k$-th order

method

either "convolution" or "recursive" (and can be abbreviated). If "convolution" a moving average is used: if "recursive" an autoregression is used. For convolution filters, the filter coefficients are for past value only.

init

specifies the initial values of the time series just prior to the start value, in reverse time order. The default is a set of zeros.

Value

mfilter returns a time series object.

Details

This is a multivariate version of "filter" function. Missing values are allowed in 'x' but not in 'filter' (where they would lead to missing values everywhere in the output). Note that there is an implied coefficient $1$ at lag $0$ in the recursive filter, which gives $$y[i,]' =x[,i]' + f[,,1] \times y[i-1,]' + ... +f[,,p] \times y[i-p,]',$$ No check is made to see if recursive filter is invertible: the output may diverge if it is not. The convolution filter is $$y[i,]' = f[,,1] \times x[i,]' + ... + f[,,p] \times x[i-p+1,]'.$$

Examples

Run this code

#AR model simulation
  ar <- array(0,dim=c(3,3,2))
  ar[,,1] <- matrix(c(0.4,  0,   0.3,
                      0.2, -0.1, -0.5,
                      0.3,  0.1, 0),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(100*3),100,3)
  y <- mfilter(x,ar,"recursive")

#Back to white noise
  ma <- array(0,dim=c(3,3,3))
  ma[,,1] <- diag(3)
  ma[,,2] <- -ar[,,1]
  ma[,,3] <- -ar[,,2]
  z <- mfilter(y,ma,"convolution")
  mulcor(z)

#AR-MA model simulation
  x <- matrix(rnorm(1000*2),1000,2)
  ma <- array(0,dim=c(2,2,2))
  ma[,,1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), 2,2,byrow=TRUE)
  ma[,,2] <- matrix(c( -0.2,  0.0,
                       -0.1, -0.3), 2,2,byrow=TRUE)
  y <- mfilter(x,ma,"convolution")
  ar <- array(0,dim=c(2,2,3))
  ar[,,1] <- matrix(c( -1.0,  0.0,
                        0.0, -1.0), 2,2,byrow=TRUE)
  ar[,,2] <- matrix(c( -0.5, -0.2,
                       -0.2, -0.5), 2,2,byrow=TRUE)
  ar[,,3] <- matrix(c( -0.3, -0.05,
                       -0.1, -0.30), 2,2,byrow=TRUE)
  z <- mfilter(y,ar,"recursive")