Re: How to estimate missing data points in a time series (financial time series e.g. stock quote, asset price)

On Dec 19, 6:46 am, "David Jones" <dajx...@xxxxxxxxx> wrote:
IRISHSTAT wrote:
On Dec 17, 1:08 pm, "arun.kumar.s...@xxxxxxxxx"
<arun.kumar.s...@xxxxxxxxx> wrote:
hi all Statisticians,

In your opinion, what is the best way exists today to estimate the
missing data points in a time series? Here my concern is estimated
data-points (as proxy for missing points) should be as accurate as
possible as well as statistically valid.

Can you please suggest me some good text books as well as online note
on that?

King regards,

One more comment . Given that you have atime series it is possible to
identify a robust ARIMA model which is then useful in making
predictions. A missing value can be predicted thus obtaining an
estimate.

Dave R

The above "making predictions" may imply only using the observations before any missing data. I guess time-series packages may do the following in a better way, and it is just a version of the suggestion by Mark Fisher, but the following would work for general patterns of missing values ...
(1) construct a covariance matrix from a fitted model for all the observations around and including the missinf values. Make the extent of the time-points included reasonable with respect to the model, and it doesn't matter if there are valid observations between the missing ones.
(2) construct the conditional covariance matrix of the missing values given the observed ones according to the usual matrix rules for the Normal distribution.
(3) used the expectation of the conditional distribution as the "infilled value"
(4) use the conditional variance to indicated the estimation error.

David Jones- Hide quoted text -

- Show quoted text -

David,

As you very politely pointed out time series approaches using the
general ARIMA form use the observations before any missing data.
However one can always reverse the process by using more recent data
to predict an older one i.e. backcasting . This is easily accomplished
by reordering the time series from latest to oldest. Iterating back
and forth like this was suggested to me by Ted Anderson of the T.W.
ANDERSON fame as a way of using "information" surrounding the missing
value.

Regards

Dave

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