perARMA (version 1.7)

parmafil: PARMA filtration

Description

Procedure parmafil filters the vector x according to matrices a, b containing PARMA model parameters. The function returns series y such that \(a(n,1)*y(n) = b(n,1)*x(n) + b(n,2)*x(n-1) + \ldots + b(n,nb+1)*x(n-nb)- a(n,2)*y(n-1) - \ldots - a(n,na+1)*y(n-na)\).

Usage

parmafil(b, a, x)

Value

Filtered signal y.

Arguments

b

matrix of size \(T \times (nb+1)\), which elements satisfy \(b(n,j)=b(n+T,j)\), usually in the literature b is called the periodic MA parameters and \(nb\) is denoted by \(q\).

a

matrix of size \(T \times na\), which elements satisfy \(a(n,j)=a(n+T,j)\), usually in the literature a is called the periodic AR parameters and \(na\) is denoted \(p\). If \(a(n,1)\) is not equal to 1 for all \(n\), the values of \(a(n,j)\) are normalized by \(a(n,j)=a(n,j)/a(n,1)\).

x

input time series.

Author

Harry Hurd

See Also

loglikec, loglikef, makeparma

Examples

b=matrix(c(1,1,0,0,.5,.5),2,3)
a=matrix(c(1,1,.5,.5),2,2)
s=sample(1:100,50, replace=TRUE)
x=matrix(s,50,1)

parmafil_out<-parmafil(a,b,x)
y=parmafil_out$y
plot(y,type="l")