Hello, as you can tell I'm a newbie here but i would appreciate your help!!!(really need it)Well i have this statement "There is no autocorrelation between daily returns, thusss daily returns are independent and identically distributed.(i.i.d)" True or False????I'm really confused.... no autocorrelation means that the returns are not uncorrelated so returns are correlated and iid is part of uncorrelated processes so the statement is false?Is my thinking completely wrong?Pls give an answer even if you think its a silly question i will definitely appreciate the effort.

AutocorrelationAutocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them. It is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal which has been buried under noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.Autocorrelation - Wikiand see also:CNL Stat AutocorrelationA second method (Moran 1947) utilizes an exact formula for the variance of the sample autocorrelation coefficient of a random process with independent, identically distributed normal errors. The theoretical formula is(see the link, towards the bottom of the page)where m is assumed to be equal to zero. Note that this formula does not depend on the autocorrelation function.The example given has to do with sunspots, but you can draw the analogy to daily returns quite easily.***So that is a start for you; perhaps others will weigh in as well. Is this something from the CFA or similar prep course?***Our user names are quite similar; I hope (for your sake) that people will not confuse you for me. But welcome to the Forum, anyway. trackstar

hello trarckstar and thank you very much for you helpthis is a part from Quantitative Finance module that i have in my bachelor degree. I think its a really hard module and sometimes i couldn't keep up with it.So if i have understood correctly what you have said to me! The statement could be true? based on the Moran method?Thank you very much for your guidanceTrekstor

i may be wrong, but for me, the answer to your question is "false"auto-correlation means that the daily returns are independent in time, but it dosn't mean (and this is where i may be wrong) that they follow the same distribution of probability (identically distributed)as an exemple: from monday to wednesday, the daily returns are independent and follow a log-normal distribution. and then on thursday and friday, they are still independant but follow a poisson distribution.does anyone can confirm that ?

hello,If auto-correlation means that dailly returns are independent then the statement is "False" since it says that there is NO auto-correlation between daily returns so they couldnt be IID...Correct?

no that's not what i said"there is no auto-correlation" means that the returns are independent, but it doesn't mean that they are identically distributed (again, to be confirmed by someone else)no auto-correlation -> independent. that's itor the question is:"no auto-correlation -> independent AND identically distributed", and this statement is wrong because of the "AND"does anyone can confirm ?

hello in your previous post you havent said no autocorrelation, thats the reason i was confused. Thanks anyway for your help.Could anyone else help here?trekstor

Price levels = auto- correlatedPrice returns = no auto - correlation (Generally in financial data) So statement in True in a text book sense... however might now ALWAYS be the case.

That is indeed part of the problem - price levels or returns.There seems to be a tendency here to accept the beginning of the statement - that returns (or do they mean levels) are *not* autocorrelated. Think this through a bit more. And separate out the statements on independence and identical distribution. (Edited: reading Traden's post below).Then on the distribution, think about a stock, maybe at 100 a share. Under normal market conditions it may waggle around 100. But if there is a market rally, market crash, specific news or an unexpected event, the price might jump. It could jump up and up or it could gap down. Jumps require some fancy footwork here, though Poisson can help.Whether or not the levels are now still evenly distributed depends on your measurement point. Think about moving averages and weighted moving averages and other methods that try to keep the mean current.Well I am focusing on price levels to dissect this and maybe this is just more confusing, if so, sorry!

Be careful here. Zero autocorrelation does NOT imply independence although independence does imply zero autocorrelation. Independence is a much stronger condition than is zero autocorrelation. IID is stronger still in adding the condition of identical distributions for each datapoint.Zero autocorrelation only means that there are no linear dependencies in the data. In contrast, some data series can have non-linear dependencies such that each datapoint is wholly deterministic from the historical data and yet the data has zero autocorrelation. A good example of this include x(t+1) = 4*x(t)*(1-x(t)) where 0 < x(t) < 1 which shows a parabolic relationship between successive datapoints but zero-autocorrelation.The point: "There is no autocorrelation between daily returns, thusss daily returns are independent and identically distributed.(i.i.d)" is false because "no autocorrelation" is not sufficient to prove "independence" and is certainly not sufficient to prove IID.

thank you very much for your help i think that i have got it now!!!

also zero autocorrelations imply independence if the underlying distribution is normal. also be careful when measuring correlations or autocorrelations. there are actually 2-3 different coefficients like kendall's or spearman's apart from the pearson's coefficient which you would have used. the other coefficients are sometimes more useful than the pearson's coefficient.