tag:blogger.com,1999:blog-325397004329727405.post7384194421387908954..comments2023-09-25T02:14:15.189-04:00Comments on Beyond Microfoundations:: More on Smoothing Splines...David R. Pughhttp://www.blogger.com/profile/09032073870730301659noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-325397004329727405.post-29338516299201050942011-06-09T13:48:50.967-04:002011-06-09T13:48:50.967-04:00I would think that the Farmer, Geanakoplos, Thurne...I would think that the Farmer, Geanakoplos, Thurner (2009) paper that I linked to in my previous post on smoothing splines (i.e., the one where I botched the confidence bands!) could be extended to create an asset pricing model that could capture the asymmetries in the returns.<br /><br />Glad to see that the post has generated some interest...David R. Pughhttps://www.blogger.com/profile/09032073870730301659noreply@blogger.comtag:blogger.com,1999:blog-325397004329727405.post-35212598826882788232011-06-09T13:33:10.909-04:002011-06-09T13:33:10.909-04:00Ivan,
The joint hypothesis testing problem you me...Ivan,<br /><br />The joint hypothesis testing problem you mention doesn't actually matter here - what's being tested is the prediction of weak-form EMH that prices should follow a random walk. The joint hypothesis problem matters when one tries to test whether an artificial portfolio can "beat the market" - so the researcher contructs a portfolio and compares its return over some period to the market return. The problem arises when you correct the accounting return on the portfolio for risk carried; this involves the use of an asset-pricing model, and hence the problem.<br /><br />The essence of EMH is the one can't beat the market using publicly available information - so the interesting question with David's result (to paraphrase your question) is why, given that returns appear to be asymmetric, can we not make an abnormal return using this information? It is interesting!Robnoreply@blogger.comtag:blogger.com,1999:blog-325397004329727405.post-56402799537622119272011-06-09T07:33:40.700-04:002011-06-09T07:33:40.700-04:00I looked at prof. Shalizi's notes to see what ...I looked at prof. Shalizi's notes to see what these splines are all about, and the idea seems to be same as in Hodrick-Prescott filter used in macroeconomics, which is interesting... and also bit reassuring (HP filter looked really ad-hoc when I first saw it). Then one starts to wonder, are there other cases where economists have reinvented the wheel?<br /><br />About EMH, I'm no expert and this is probably outside the scope of your blogpost, but in general testing EMH means testing jointly efficiency / rational expectations and a particular asset pricing model (since you can have model where expected returns vary over time in response to macroeconomic factors). So maybe there exists a model which would explain such an asymetric dynamics without violating EMH... and maybe not. It's certainly an interesting question!ivansmlnoreply@blogger.comtag:blogger.com,1999:blog-325397004329727405.post-25268981071013613002011-06-08T18:54:30.595-04:002011-06-08T18:54:30.595-04:00Cosma,
Thanks for the excellent comment (and more...Cosma,<br /><br />Thanks for the excellent comment (and more importantly thanks for putting your lecture notes online). I am really enjoying learning about non-parametric estimation....didn't get a lot of it in my courses on econometrics!David R. Pughhttps://www.blogger.com/profile/09032073870730301659noreply@blogger.comtag:blogger.com,1999:blog-325397004329727405.post-27458687478259653572011-06-08T15:00:54.442-04:002011-06-08T15:00:54.442-04:00Yes, you really can't just re-sample individua...Yes, you really can't just re-sample individual data points for time series, because it destroys the dependencies you are trying to capture. Re-sampling residuals is one reasonable approach. Another is to re-sample whole blocks of observations, producing a surrogate time series with the right dependence within each block (and hopefully close to the right dependencies over-all, if correlations decay quickly). There is a bias/variance trade-off which controls the optimal block length; theory says it should grow like the cube root of the duration of the time series, but then you get into finding the constant. (See <a href="http://cscs.umich.edu/~crshalizi/weblog/algae-2010-05.html#lahiri" rel="nofollow">Lahiri</a> for gory details.) My recollection was that a block length of 4 days was optimal for the daily returns, when I did that example.<br /><br />Robustness: You could try more robust fitting methods (like using mean absolute error, rather than mean-squared error, in the spline). Or just removing those particular data points. But I'd be very leery of doing that; those days really happened. (To steal one of D^2's lines, the Great Depression was not an unusually noisy observation of an underlying 3% trend growth rate.)Cosma Shalizihttp://bactra.org/weblog/noreply@blogger.com