The function may be called by the names: g13bdc, nag_tsa_multi_transf_prelim or 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 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 and , as defined in the description of g13bac, should be used in place of those between and .
The estimates are obtained by solving for the equations
where the ‘’ is used for and ‘’ 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
1: – doubleInput
On entry: the cross-correlation between the two series at lag , .
2: – const doubleInput
On entry: the cross-correlations between the two series at lags to ,
, for .
, for .
3: – IntegerInput
On entry: , the number of lagged cross-correlations in the array r.
4: – Nag_TransfOrder *Input
On entry: 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.
5: – doubleInput
On entry: the ratio of the standard deviation of the series to that of the series, .
6: – doubleOutput
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 .
7: – 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.
8: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
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 for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, .
On entry, .
On entry, and .
Equations used in the computations may become unstable, in which case results are reset to zero with array isf values set accordingly.
8Parallelism and Performance
g13bdc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
g13bdc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The time taken by 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.