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In the paragraph before the one from which you gave the quotation is written such a thing: “…when u_i^2 is high, there is a tendency for u_(i+1)^2, u_(i+2)^2, … to be high; when u_i^2 is low, there is a tendency for u_(i+1)^2, u_(i+2)^2, … to be low.” This means that they (u_(i+1)^2,u_(i+1)^2, u_(i+2)^2,…) are correlated. Which by itself means that u_i^2 ...


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It is not entirely clear what you're after, since Method 1 from the question is a statistical model, while Method 2 is a statistical test. From the initial question, I'm going to make the assumption that what you're actually after is some number that summarises "momentum" on a given day. If this is the case, I would weakly prefer the Ljung-Box test ...


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The high serial correlation you are getting in the first case is a spurious correlation. The correct way to do it is with returns. The price series has a unit root. You need to take diff(log(prices))) in order to have a stationary time series, on which you can then estimate autocorrelations, auto regressive coefficients, etc. properly. This was shown by ...



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