In sci.stat.consult Rich Ulrich <[EMAIL PROTECTED]> wrote:
> - since no one else is saying anything, and it seems messy -
> On Wed, 9 Oct 2002 18:53:30 +0000 (UTC), Ronald Bloom
> <[EMAIL PROTECTED]> wrote:
>>
>> Suppose one has applied *univariate* time-series methods to a handful
>> of data series separately,
> By 'univariate time-series', do you refer to autocorrelation alone?
> or to spectral analyses?
for instance: ARIMA models fit to the univariate streams; or state-space
structural models fit to the univariate streams.
>>
>> Can the multiple post-forecast residuals be sensibly treated
>> by a suite of classical *multivariate* inferential techniques?
>>
> Which is 'multiple post-forecast' here? - a series of predictions,
> or (say) some single cross-section on that 'handful of series' ?
Post forecast residuals: presuming that model selection and
model fitting have been done well, the post-forecast residuals
should look like i.i.d non serially correlated gaussian variates.
The schematic looks like this:
Y_1(t) -> [Forecast Scheme 1] -> R_1(t)
Y_2(t) -> [Forecast Scheme 2] -> R_2(t)
.
.
Y_2(t) -> [Forecast Scheme N] -> R_N(t)
Where the Y_k(t) are the raw data, the R_k(t) are the respective
post-forecast i.i.d "supposedly" gaussian residuals.
The question concerns the treatment of the *vector* series
consisting {R_1(t),R_2(t),...,R_N(t)}
Although each R_k(t) is an I.I.D. series (at least until it is decided
that the k-th model no longer holds good) the covariance structure
is by no means trivial.
At any rate, in this schema, the covariance structure across series
was ignored, the time-series models are not vector autoregressions
or anything comparable. The question is, essentially, can one
make up for *not* having fit the aggregate by vector forecasting
scheme (avoiding the need to fit simultaneously zillions of
unobservable covariance parameters by M.L. estimation) and
do straightforward multivariate analysis on the vector of
post-forecast residuals, which retain the covariance structure
that was not taken into account when doing the univariate fits?
.
.
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