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Jul 27, 2015 at 2:15 comment added Barnaby I agree, in the paper there are some mathematical explanations. What I imply by the question is that once denoised the signal the left coefficient of the signal is either a series of zeros or very small coefficients.
Jul 26, 2015 at 23:45 comment added Colin T Bowers @Barnaby I'm not sure I understand the question. I'll try and find the time to come back soon and give my interpretation of an answer. But I'll need to have a quick skim of the paper you've referenced first, which is why I need a bit of time :-) I do think the discussion needs a formal (mathematical) definition of white noise, which I'm assuming I'll get from the paper.
Jul 26, 2015 at 16:23 comment added Barnaby @ColinTBowers - Can we say therefore that the above assumption implies that the distribution of white noise and that distribution of the signal for stock indexes is approximatedly the same?
Jul 23, 2015 at 1:10 comment added Colin T Bowers @Barnaby Understood. The problem I refer to can potentially apply to any portfolio of more than one asset, if one examines returns constructed from end-of-day prices. I think your question is an interesting one, by the way, and I might come back and have a crack at a second answer if I get some spare time over the next week or two. Cheers.
Jul 22, 2015 at 10:38 comment added Barnaby @ColinTBowers - I referred to traditional portfolios in the asset management sense where a few tens of stocks are poled toguether and deviation on weights to the main idexes that serve as benchmarks are provided by a basis of stratetgic and tactical frameworks
Jul 22, 2015 at 4:07 comment added Colin T Bowers @Barnaby A stock index such as the S&P500 is a portfolio. The "spurious" autocorrelation problem due to thin trading definitely exists in indices prior to the 70's. Also, if you want me to see your comment, you need to preface it with the "at" symbol followed immediately by my username (no spaces) or else I won't receive a notification. I just happened to come back to this page for a different reason and saw your comment. Cheers -colin.
Jul 22, 2015 at 1:36 comment added Barnaby The tests were done on S&P500 and other derived stock indexes, however not portfolios
Jul 22, 2015 at 0:59 comment added Colin T Bowers @Barnaby Also, a lot of the tests pre 70s were done on stock indices or portfolios. Thin trading in the underlying components of the indices led to "spurious" autocorrelation in the index series itself. I think the classic paper on this is Dimson (1979) "Risk Measurement When Shares are Subject to Infrequent Trading"
Jul 21, 2015 at 18:49 comment added Andrew Institutional change (e.g. new hedging derivatives, freer capital flows, electronic trading) could account for this. Markets became more efficient and as a result the arbitrage opportunities (serial correlation) were eliminated from the data as the variance of returns was reduced.
Jul 21, 2015 at 17:18 comment added Barnaby White noise has constant amplitude (amplitude that varies with time has a corresponding frequency spectrum) and does not change amplitude, while in the article speaks about a permanent change in the amplitude as per after the 70s from that of pre 70s interpreted from the change of the level of significance in pre 70s close to rejection rates to post 70s well below the rejection of the white noise null hipothesis
Jul 21, 2015 at 14:45 history answered Andrew CC BY-SA 3.0