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Re: st: RE: Allowing different lag lengths by country in an error correction model with panel data

From   Nick Cox <>
Subject   Re: st: RE: Allowing different lag lengths by country in an error correction model with panel data
Date   Tue, 12 Feb 2013 22:19:15 +0000

That's a very useful list. However, I am not clear that irregular
spacing means the same thing to everyone.

Some notes follow. Sorry, but this is unlikely to be much use to the
original poster.

I can think of various meanings.

1. Data would be regularly spaced (every day, month, year, whatever)
except that there are missings
and the missingness is what imparts the irregularity.

1a. The missings are gaps but not really missings in the strong sense
that anything happened (notably, there was no business at weekends or
on public holidays). The known technology here is positive, using a
business calendar.

1b. The missings represent values that were lost or never measured (in
hydrology the biggest floods can be too big to measure for safety
reasons, or the apparatus was submerged or destroyed, etc.).

1a and 1b naturally do not exclude each other.

This category nevertheless grades seamlessly into

2. Series measured so capriciously that filling in gaps is hopeless;
we just have to do the best we can. The environmental sciences hold
many examples dependent on when people could do field measurements.
Biases to certain times of year or week or day are then

3. Series in which the generating process imparts itself all the
irregularities, and the carelessness or capriciousness of observers is
not the issue. Dates of birth of a mother's children, strikes,
earthquakes, eruptions, releases of Stata, etc., etc. Some would want
to call these series realisations of point processes or series of
events, not time series. Nevertheless they often feature magnitudes as
well as times: weight of baby, number of workers involved, magnitude
of earthquake, volume of rock blasted, number of pages in the manuals,
etc., etc.

More positively, there is a whole literature mostly outside statistics
on how to estimate spectra from irregular data. The main roots appear
to be in astronomy and geodesy. The key terms are least-squares or
Lomb-Scargle (-ls- either way). I have a crude Stata program not ready
for release. I've even seen an argument that highly irregular times of
observation are better for spectral analysis because aliasing doesn't
bite so hard.

A venerable astronomical time series from Whittaker and Robinson's
Calculus of observations has been passed
down with the time series community to be the sandpit for many a new
technique. Harold Jeffreys in his inimitable Theory of probability
(Oxford University Press 1961) points out that the series implies
cloud-free conditions for observation every day for some years,
something implausible for the implied location. I've never seen that
remark quoted.


On Tue, Feb 12, 2013 at 9:14 PM, Millimet, Daniel <> wrote:

> There is a lengthy literature in time series models with irregular spacing.  The literature on dynamic panel models is smaller and the problem is complex.

[several useful references]
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