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Some say the presence of autocorrelation (aka serial correlation) in a stock's financial return time series helps with forecasting its next-day movements, unlike a stock that has low serial correlation between its return observations.

Does this mean that a stock with high serial correlation should be weighted more heavily in a portfolio with other stocks that have lower serial correlation than it? Why?

What if the stock with high serial correlation has a lousy Sharpe ratio?

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    $\begingroup$ From a (narrow...) mathematical point of view we could model the return series as VAR(p) processes and employ some of the machinery from the source below in order to come up with (conditional or unconditional) expected value vectors and covariance matrices. We could then show how the AR parameters influence an optimal portfolio (but only in the mean/covariance sense, though). Another path could be some intertemporal optimization process, but that would require some more machinery I think. asc.ohio-state.edu/de-jong.8/note6.pdf $\endgroup$ Feb 4, 2021 at 7:48
  • $\begingroup$ @KermittFrog: Hi. That looks like a good set of notes but do you know how to access all of them ? I ask because they look like class notes probably. I tried to just take out the note6.pdf part but that didn't work. Thanks. $\endgroup$
    – mark leeds
    Feb 4, 2021 at 17:15
  • $\begingroup$ Sorry, that just came up from a google search $\endgroup$ Feb 4, 2021 at 17:46
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    $\begingroup$ no problem. still a nice set of notes. probably a good class !!!! develarist: one thing I didn't see mentioned was that you have to see if the autocorrelation is helpful for forecasting because one doesn't imply the other ( because time-frame matters ). $\endgroup$
    – mark leeds
    Feb 4, 2021 at 20:32

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Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little.

One obvious question is whether your AC process is strong enough to overcome transaction costs and slippage, if markets are almost-random. Then someone trying to trade that could easily just get their position sizes whipsawed for little or negative net gain.

Then there's the question of what your autocorrelated AR(1) process looks like, if you look at it from an AR(2) perspective. How consistent is the correlation of T-1 and T-2 implied by the betas here with the correlation of T-2 and T-3? The latter being T-1 versus T-2 with one day's lag, does the autocorrelation process change to something different overnight?

To which the answer I'd give, if I were asking your own question myself, would be that there could be a serial momentum effect. But that it was a broader issue than a daily AR(1) process. The underlying process was more like a 65-200d undercurrent.

The problem trying to model trading this are obviously intra-period corrections. You are faced with a menu of momentums; and which are the more relevant?

Put in its most horrible possible way, an AR(200) process that allows for a slow autocorrelation process creates 200x200/2 = 20,000 interactions between your lagged variables. You don't have a p>n regression problem, because you're only looking back 200 days and thus have 200 inputs. But it's a massive incentive for the model/fit to overfit through multicollinearity.

I merely suggest that the investment-related industries are overweight econometricians; and if they hadn't tried to find some ARCH, GARCH, ARMA, ARIMA, etc. "secret sauce" to markets on their own time, they'd probably already have been fired. But yet momentum still seems to be a "thing". A thing that pisses these people off like no other, precisely because it defies modelling. It defies rational explanation theoretically; while being so tantalisingly beyond reach ;-)

To your actual question, even if the momentum effect was real and measurable, then - THEORETICALLY - this should NOT cause you overweight such assets. The reason being that the invalidation of random residuals pretty much blows the traditional mean-variance framework for asset allocation out of the water from the get-go. Pragmatically - if it works, of course you should buy them and avoid the rest. But your answer to how much is predicated on a random process that is no longer random! Null that hypothesis; and you need to re-invent asset allocation... that's the real problem here.

keep well, DEM

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  • $\begingroup$ Your last passage made me stop modelling this in a (conditional) Markowitz ansatz. Nice. $\endgroup$ Feb 4, 2021 at 7:49
  • $\begingroup$ Conditional Markovs are OK, @Kermitfrog. Quantum portfolios for each potential regime are fine, just so long as you don't ever stop and look at their performance, crashing the probability density wave ;-) $\endgroup$
    – demully
    Feb 4, 2021 at 8:32

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