# R_w_ma: Covariance matrix for PARMA model (conditional) In perARMA: Periodic Time Series Analysis

 R_w_ma R Documentation

## Covariance matrix for PARMA model (conditional)

### Description

Procedure R_w_ma computes the covariance matrix of the moving average part of a PARMA sequence. This is used in maximum likelihood estimation in conjunction with the Ansley transformation method of computing the likelihood of the sample conditioned on the firt m = max(p; q) samples being ignored (or set to null); see Ansley or Brockwell and Davis for background on the procedure. The method avoids the cumbersome calculation of full covariance matrix.

### Usage

R_w_ma(theta, nstart, nlen)

### Arguments

 theta matrix of size T \times (q+1) contains vectorial parameters [\theta_0,\theta_1,...,\theta_q], where \theta(0,t)=\sigma(t)=del(t), thus theta = [del,theta_1,...,theta_q]. nstart starting time, for conditional likelihood in PARMA set to p+1. nlen size of the covariance matrix.

### Details

Procedure R_w_ma implements calculation of covariance matrix of size nlen-p from the parameters theta and phi of PARMA sequence. The result is returned as two vectors, first containing non-zero elements of covariance matrix and the second containing indexes of this parameters. Using these vectors covariance matrix can be easily reconstructed.

### Value

procedure returns covariance matrix in sparse format as following:

 R vector of non-zero elements of covariance matrix. rindex vector of indexes of non-zero elements.

Harry Hurd

### References

Ansley, (1979), An algorithm for the exact likelihood of a mixed autregressive moving average process, Biometrika, v.66, pp.59-65.

Brockwell, P. J., Davis, R. A. (1991), Time Series: Theory and Methods, 2nd Ed., Springer: New York.

loglikec, loglikef

### Examples

T=12
nlen=480
p=2
a=matrix(0,T,p)
q=1
b=matrix(0,T,q)
a[1,1]=.8
a[2,1]=.3

phia<-ab2phth(a)
phi0=phia$phi phi0=as.matrix(phi0) b[1,1]=-.7 b[2,1]=-.6 thetab<-ab2phth(b) theta0=thetab$phi
theta0=as.matrix(theta0)
del0=matrix(1,T,1)

R_w_ma(cbind(del0,theta0),p+1,T)

perARMA documentation built on Nov. 17, 2023, 9:06 a.m.