NAG Library Function Document
nag_tsa_transf_prelim_fit (g13bdc) calculates preliminary estimates of the parameters of a transfer function model.
||nag_tsa_transf_prelim_fit (double r0,
const double r,
nag_tsa_transf_prelim_fit (g13bdc) calculates estimates of parameters
in the transfer function model
given cross-correlations between the series
and lagged values of
and the ratio of standard deviations
, as supplied by nag_tsa_cross_corr (g13bcc)
It is assumed that the series
used to calculate the cross-correlations is a sample from a time series with true autocorrelations of zero. Otherwise the cross-correlations between the series
, as defined in the description of nag_tsa_arma_filter (g13bac)
, should be used in place of those between
The estimates are obtained by solving for
where the ‘
’ is used for
Any value of arising in these equations for is taken as zero. The parameters are checked as to whether they satisfy the stability criterion.
Box G E P and Jenkins G M (1976) Time Series Analysis: Forecasting and Control (Revised Edition) Holden–Day
r0 – doubleInput
On entry: the cross-correlation between the two series at lag , .
r[nl] – const doubleInput
On entry: the cross-correlations between the two series at lags to , , for .
, for .
nl – IntegerInput
, the number of lagged cross-correlations in the array r
transfv – Nag_TransfOrder *Input
: the orders of the transfer function model where the triplet (transfv. nag_b
, transfv. nag_q
, transfv. nag_p
) corresponds to the triplet
as described in Section 2.3.1
in the g13 Chapter Introduction.
s – doubleInput
On entry: the ratio of the standard deviation of the series to that of the series, .
wds – doubleOutput
the dimension, dim
, of the array wds
must be at least
On exit: the preliminary estimates of the parameters of the transfer function model in the order of MA-like parameters followed by the AR-like parameters. If the estimation of either type of parameter fails then these arguments are set to .
isf – IntegerOutput
On exit: indicators of the success of the estimation of MA-like and AR-like parameters respectively. A value indicates that there are no parameters of that type to be estimated. A value of or indicates that there are parameters of that type in the model and the estimation of that type has been successful or unsuccessful respectively. Note that there is always at least one MA-like parameter in the model.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
On entry, argument had an illegal value.
On entry, .
On entry, .
On entry, .
On entry, , , and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
On entry, r0
On entry, .
On entry, lies outside : and .
Equations used in the computations may become unstable, in which case results are reset to zero with array isf
values set accordingly.
The time taken by nag_tsa_transf_prelim_fit (g13bdc) is roughly proportional to .
This example reads the cross-correlations between two series at lags to . It then reads a transfer function model and calculates and prints the preliminary estimates of the parameters of the model.
9.1 Program Text
Program Text (g13bdce.c)
9.2 Program Data
Program Data (g13bdce.d)
9.3 Program Results
Program Results (g13bdce.r)