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.TH lattn 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
lattn - recursive solution of normal equations
.SH CALLING SEQUENCE
.nf
[la,lb]=lattn(n,p,cov)
.fi
.SH PARAMETERS
.TP
n
: maximum order of the filter
.TP
p
: fixed dimension of the MA part. If \fVp= -1\fR,
the algorithm reduces to the classical Levinson recursions.
.TP
cov
: matrix containing the \fVRk\fR's (\fVd*d\fR matrices for
a d-dimensional process).It must be given the
following way
.IG
.nf
| R0 |
| R1 |
cov=| R2 |
| . |
| . |
|Rnlag|
.fi
.FI
.LA $$ cov = \left[ \matrix{ R_0 \cr R_1 \cr R_2\cr
.LA \vdots \cr R_{nlag}}
.LA \right] $$
.TP
la
: list-type variable, giving the successively calculated
polynomials (degree 1 to degree n),with coefficients Ak
.SH DESCRIPTION
solves recursively on \fVn\fR (\fVp\fR being fixed)
the following system (normal equations), i.e. identifies
the AR part (poles) of a vector ARMA(n,p) process
.IG
.nf
|Rp+1 Rp+2 . . . . . Rp+n |
|Rp Rp+1 . . . . . Rp+n-1|
| . Rp . . . . . . |
| |
|I -A1 -A2 . . .-An|| . . . . . . . . |=0
| . . . . . . . . |
| . . . . . . . . |
| . . . . . . . Rp+1 |
|Rp+1-n. . . . . . Rp |
.fi
.FI
.LA $$ \left( \matrix{ I & -A_1 & -A_2 & \ldots & -A_n
.LA } \right)
.LA \left( \matrix{ R_{p+1} & R_{p+2} & \ldots & R_{p+n} \cr
.LA R_p & R_{p+1} & \ldots & R_{p+n-1} \cr
.LA \vdots & \vdots & \ldots & \vdots \cr
.LA R_{p+1-n} & R_{p+2-n} & \ldots & R_{p} \cr
.LA } \right) = 0 $$
where {\fVRk;k=1,nlag\fR} is the sequence of empirical covariances
.SH AUTHOR
G. Le V.
|
