A question about: Kalman in R, time series and
deJong-Penzer statistic - how to compute it using
available artefacts of KalmanXXXXX?
Background. in the paper
http://www.lse.ac.uk/collections/statistics/documents/researchreport34.pdf
'Diagnosing Shocks in TIme Series', de Jong and Penzer
construct a statistic (tau) which can be used to
locate potential shocks. [p15, Theorem 6.1 and below].
They also state that all the components of that
statistic (v_i, F_i, r_i, N_i) 'are computed with
Kalman Filter Smoother applied to the null model'.
Also, as I understand, that part has been implemented
in one of the S packages , SsfPack, as the book on
that states on p 531 'the standardized smoothed
disturbances may be interpreted as t-statistics for
impulse intervention variable in the transition and
measurement equations.' and equations for the
statistic are:
eta_t / sqrt(var(eta_t),
where eta_t and var have hats over them. The second
equation is identical, with 'eta' replaced by
'epsilon'. On page 524 we also have:
"the smoothed disturbance estimates are the estimates
of the measurement equation innovations epsilon and
transition equation innovations eta based on all
available information Y. ... the computation of
hat(eta) and hat(epsilon) from the Kalman smoother
algorithm is described in Durbin and Koopman chapter
7, 'Time series analysis by state space methods', OUP
(2001) "
Local libraries do not have this book and it will take
several weeks to get it.
Assuming I will get the book: does the KalmanXXX set
of functions produce all the necessary artefacts to
compute this statistic either as per deJong-Penzer or
as per SsfPack?
Reading carefully through the manual I see that we
have artefacts of states and normalized residuals
(presumably of states - but how can I unscale them if
I need them)? What about other stats? How to compute
smoothed disturbance estimates?
I am rather confused - that's my first approach to
Kalman filter and state models.
