Estimate impulse response using prewhitenedbased correlation analysis
ir=cra(data)
[ir,R,cl]
= cra(data,M,na,plot)
estimates
the impulse response for the timedomain data, ir
=cra(data
)data
.
[
estimates
correlation/covariance information, ir
,R
,cl
]
= cra(data
,M
,na
,plot
)R
, and the
99% confidence level for the impulse response, cl
.
The cra
command first computes an autoregressive
model for the input u as $$A(q)u(t)=e(t)$$,
where e is uncorrelated (white) noise, q is
the timeshift operator, and A(q)
is a polynomial of order na
. The command then
filters u and output data y with A(q)
to obtain the prewhitened data. The command then computes and plots
the covariance functions of the prewhitened y and u and
the crosscorrelation function between them. Positive values of the
lag variable then correspond to an influence from u to
later values of y. In other words, significant
correlation for negative lags is an indication of feedback from y to u in
the data. A properly scaled version of this correlation function is
also an estimate of the system impulse response. This is also plotted
along with 99% confidence levels. The output argument ir
is
this impulse response estimate, so that its first entry corresponds
to lag zero. (Negative lags are excluded in ir
.)
In the plot, the impulse response is scaled so that it corresponds
to an impulse of height 1/
T and
duration T, where T is the sample
time of the data.

Inputoutput data. Specify


Number of lags for which the covariance/correlation functions are computed.
Default: 20 

Order of the AR model to which the input is fitted. For the prewhitening, the input is fitted to an AR model of
order Use Default: 10 

Plot display control. Specify plot as one of the following integers:
Default: 1 

Estimated impulse response. The first entry of 

Covariance/correlation information.


99 % significance level for the impulse response. 
An often better alternative to cra
is impulseest
, which use a highorder FIR
model to estimate the impulse response.
impulse
 impulseest
 spa
 step