-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Devon McCormick <[email protected]> writes:
> Quantiles are a very useful way to compare stochastic models, e.g. what's > the performance of bottom-decile PE stocks versus top-decile ones? And if > there is a consistent relation between the top and bottom deciles, does it > also hold if we use 11-tiles or 9-tiles? Note that Tukey, in Understanding Robust and Exploratory Data Analysis, uses fourths instead of quartiles (perhaps someone mentioned it here, but, if so, I missed it). Devon, you bring up a question I've been puzzling about recently when you mention stocks. The Shannon Nyquist sampling theorem says one has to sample at twice the highest frequency of energy in the signal we're measuring, and (a little) research I've found by Hinich and by someone else at the Federal Reserve building on that suggests that stocks have significant energy at frequencies above daily. Thus modeling unfiltered closing prices would seem to give erroneous results. It's not limited to stock prices, though; presumably quarterly business results, economic indicators, and others could all suffer from the same problem. That's challenging, though. In some domains, it's very expensive to collect the data at a high enough frequency. If you can gather the fully sampled data, then you can filter and decimate it to reduce the sample rate of the final data to that which you would like. Do you have insights to suggest how much this problem is known amongst those who do model time series professionally? I don't see mention of it, for example, in my copy of the Box - Jenkins Time Series Analysis. Bill - -- Bill Harris http://facilitatedsystems.com/weblog/ Facilitated Systems Everett, WA 98208 USA http://facilitatedsystems.com/ phone: +1 425 374-1845 -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) iEYEARECAAYFAkrcaSIACgkQ3J3HaQTDvd8o6gCfWwY/GEMvX+1sVNJEc6ZAVnKj CaAAn1cd1lPfBhXT/IqmmfYUEBis7u2h =Wy5D -----END PGP SIGNATURE----- ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
