perARMA (version 1.4)

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)

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 normali

x

input time series.

Value

• Filtered signal y.

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")