parmaf {perARMA} | R Documentation |
PARMA coefficients estimation
Description
Procedure parmaf
enables the estimation of parameters of the chosen representation of PARMA(p,q) model. For general PARMA we use non-linear
optimization methods to obtain minimum of negative logarithm of likelihood function using loglikef
procedure. Intitial values of parameters are computed using Yule-Walker equations.
Usage
parmaf(x, T_t, p, q, af, bf, ...)
Arguments
x |
input time series. |
T_t |
period length of PC-T structure. |
p |
maximum PAR order, which is a number of columns in |
q |
maximum PMA order, which is a number of columns in |
af |
|
bf |
|
... |
Other arguments: |
Details
In order to obtain maximum likelihood estimates of model parameters a
and b
we use a numerical optimization method to minimalize value of y
(as negative value of logarithm of loglikelihood function returned by loglikef
)
over parameter values. Internally, parameters a
and b
are
converted to phi
and theta
as needed via function
ab2phth
. For the present we use optim
function with defined method="BFGS"
(see code for more details).
Value
list of values:
a |
is matrix of Fourier coefficients determining |
b |
is matrix of Fourier corfficients determining |
negloglik |
minimum value of negative logarithm of likehood function. |
aicval |
value of AIC criterion. |
fpeval |
value of FPE criterion. |
bicval |
value of BIC criterion. |
resids |
series of residuals. |
Author(s)
Harry Hurd
References
Box, G. E. P., Jenkins, G. M., Reinsel, G. (1994), Time Series Analysis, 3rd Ed., Prentice-Hall, Englewood Cliffs, NJ.
Brockwell, P. J., Davis, R. A., (1991), Time Series: Theory and Methods, 2nd Ed., Springer: New York.
Jones, R., Brelsford, W., (1967), Time series with periodic structure, Biometrika 54, 403-408.
Vecchia, A., (1985), Maximum Likelihood Estimation for Periodic Autoregressive Moving Average Models, Technometrics, v. 27, pp.375-384.
See Also
Examples
######## simulation of periodic series
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
a[1,2]=-.9
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)
makeparma_out<-makeparma(nlen,phi0,theta0,del0)
y=makeparma_out$y
## Do not run
## It could take more than one minute
############ fitting of PARMA(0,1) model
p=0
q=1
af=matrix(0,T,p)
bf=matrix(0,T,q+1)
bf[1,1]=1
bf[1:3,2]=1
parmaf(y,T,p,q,af,bf)
########### fitting of PARMA(2,0) model
p=2
q=0
af=matrix(0,T,p)
bf=matrix(0,T,q+1)
af[1:3,1]=1
af[1:3,2]=1
bf[1,1]=1
parmaf(y,T,p,q,af,bf)
############ fitting of PARMA(2,1) model
p=2
q=1
af=matrix(0,T,p)
bf=matrix(0,T,q+1)
af[1:3,1]=1
af[1:3,2]=1
bf[1,1]=1
bf[1:3,2]=1
parmaf(y,T,p,q,af,bf)