naginterfaces.library.tsa.multi_​transf_​prelim

naginterfaces.library.tsa.multi_transf_prelim(r0, r, nna, s)[source]

multi_transf_prelim calculates preliminary estimates of the parameters of a transfer function model.

For full information please refer to the NAG Library document for g13bd

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g13/g13bdf.html

Parameters
r0float

The cross-correlation between the two series at lag , .

rfloat, array-like, shape

The cross-correlations between the two series at lags to , , for .

nnaint, array-like, shape

The transfer function model orders in the standard form (i.e., delay time, number of moving-average MA-like followed by number of autoregressive AR-like parameters).

sfloat

The ratio of the standard deviation of the series to that of the series, .

Returns
wdsfloat, ndarray, shape

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 .

isfint, ndarray, shape

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.

Raises
NagValueError
(errno )

On entry, , and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, , , and .

Constraint: .

(errno )

On entry, and .

Constraint: .

Notes

multi_transf_prelim 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 multi_xcorr().

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 multi_filter_arima(), should be used in place of those between and .

The estimates are obtained by solving for the equations

then calculating

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.

References

Box, G E P and Jenkins, G M, 1976, Time Series Analysis: Forecasting and Control, (Revised Edition), Holden–Day