
What is the usual way of measuring a market's tendency to meanrevert? I'd like to have a way to quantitatively express how meanreverting or trending a given time period was.
I'm interested in timescales from a few seconds to an hour or two, although I doubt that will affect the metric I should use. 




Scotty


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You need to research into Tim Bollerslev et al, and "realized volatility". 
“Whatever you do, or dream you can, begin it. Boldness has genius and power and magic in it.” 


 

Baltazar


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that's a very well topic from the theoretical side at least. Look "variance ratio test" "hurst exponant"
these are statistical quantities, they can't tell you how trendy a specific run was. i mean 10 days of +1% in a row can still be produced by a mean reversion process except with very low probability compared to being produced by a trending process.
I mean it's the usual estimation of process parameters from realizations problem anyway.
edit: this can be a good start http://www.ljmu.ac.uk/AFE/AFE_docs/VR_AND_REGR.PDF

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cquand


Total Posts: 91 
Joined: Sep 2007 


one method maybe
you take a time series with a given frequency over say 1 hour, calculate several realized vol over that period with different frequency of return (every 1min, 2min, 5 min...): look at the realized vol "Term (Frequency?)" Structure: the more downward sloping, the more meanreverting 




Baltazar


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yep, that's what variance ratio methods are about, calculate variance at different sampling frequency, check if the ratio scale with sqrt(t) as it should for brownian motion.
the scaling factor gives you the Hurst exponent, so you can estimate the trending tendency. You can use other method to estimate such ratios, such as wavelet based ones.
Due to microstructure this approach can probably not used on too high frequency. Papers recommend not to sample faster than 15 minutes if you work with last traded. You can go faster but you need to take microstructure into account. If you don't you'll see the high freq vol is very high compared to lower freq one. 
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I understand that last traded will tend to "bounce" on shorter time scales.
On liquid markets, does using the market midpoint allow me to go to much shorter time scales? I'm thinking of sampling once/minute. 




MrMagoo


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Andy Lo has an article about it on his "nonrandom walk down wall street" old book. The book is freely downloadable somewhere in the web. I read many years ago.
The variance ratio test is simple, just compare vols at different frequencies and define a threshold ratio level to label the market as "trending" or "MR".
Many useful real time stuff can be adapted for trading, with other models based on ML ,hidden markov, etc. but that can be a bit more difficult. 
"One who says it can't be done should not interrupt the person doing it."



NIP247


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Joined: Feb 2005 


HockeyPlayer, the question is really what the aim of the study is. If you're sampling at higher frequency (with all caveats mentioned), you'll probably come to evident conclusions like "it pays to be a market maker if you can buy at the bid and sell at the offer all day long...". IMHO you have to choose a relevant sampling frequency and period with respect to what you are trying to detect/achieve/trade. 
On your straddle, done on the puts, working the calls... 




I'm working through the Lindemann paper that Baltazar linked and I wanted to discuss his creation of synthetic timeseries (to test the Variance Ratio's power):
"Each type of time series is represented by a portfolio of 100 artificially created series. Each series consists of 500 values (interpreted in the following as daily percentage changes or simply returns). The ‘random’ portfolio was created by sampling the daily changes from a normal distribution (N(0,1)). The ‘trending’ series were generated by sampling from a normal distribution, this time with a mean different from zero (N(0.15,1)). The creation of the ‘mean reverting’ series has been done by also sampling the returns from a normal distribution (N(0,1)), but in addition subtracting 0.2% when the return was positive and added 0.2% when the return was negative."
I'm ok with his trending series, although I'd prefer a series that trended both up and down. But I feel like his mean reverting series is wrong. I read his approach as being equal to just taking 80% of the value that N(0,1) gives. That gives cumulative returns closer to 0, but doesn't help with mean reversion. I think a better approach would be to skew the distribution positive when the previous values sum to a negative and viceversa. 



Baltazar


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Regarding a serie that trend ups and downs, it introduces a problem of scale: if you make your serie trend up one month, then down another month, on a low frequency view your serie will actually be mean reverting. By doing only uptrend, he makes sure it is trendy at all horizons.
taking 80% of what return gives would be just working on the variance. I guess what he means (but i should check the paper) is substract .2 when previous day was up and add .2 when previous day was down. this way it is strictly mean reverting on a one day horizon but with no further memory. what you suggest would create stronger mean reversion because the mean of the next return would be function of all past returns up to now.

Qui fait le malin tombe dans le ravin 




MrMagoo: "The variance ratio test is simple, just compare vols at different frequencies and define a threshold ratio level to label the market as "trending" or "MR"."
Let's say i've got different returns for different time frames. I am calculating vols (i'm using a nonparametric model) using weekly, 30 days , 15 days and 5 days returns. I then annualize the results by timing everything for sqrt(252) and then compare the results.
If the vols are more or less the same ,numerically and directionally speaking, the market should trend otherwise the opposite relation should hold.
is the procedure correct? is the interpretation right or i am missing something?
How can i define the threshold ratio level in a quantitative way? should i see how the ratio moves and then rank it?
sorry if these questions are a bit naive. The test is intuitively simple but i do not know if i am doing it right.

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MrMagoo


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@Hyper
Another way to see this test, it is an attempt to "quantify" the autocorrelation of a given timeseries and a given sample. It suffers from all the known financial econometrics estimation problems.
If the vols are more or less the same ,numerically and directionally speaking, the market should trend otherwise the opposite relation should hold.
A greater than 1 ratio would theoretically point to (insample) positive autocorrelation, thats "trending" within the larger estimation period.
How can i define the threshold ratio level in a quantitative way? should i see how the ratio moves and then rank it?
Broadly speaking, the practical trading problem is how to read a test statistic, given the sample distribution of that statistic. For a taste from the quant side, read this paper up to the end of section I.
I believe statistical learning research can be useful concerning this specific task, so thats what i meant by threshold level and labeling. 
"One who says it can't be done should not interrupt the person doing it."





@ MrMagoo: thanks a lot for the explanation and for the paper....it's much clearer now 
WWW.HYPERVOLATILITY.COM 


catman


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Joined: Oct 2012 


This isn't answering your question, but it's a related question. In herding studies the question is asked "under what conditions do investors form consensus views?", and the question is whether the constituents of the market herd around a shared mean in high volatility, extreme return, low/high liquidity, etc periods.
Just search for "herding" in your literature database to learn more. 




Jurassic


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> you'll probably come to evident conclusions like "it pays to be a market maker if you can buy at the bid and sell at the offer all day long...".
Why is this evident? 


